{"id":6632,"date":"2021-12-10T03:17:27","date_gmt":"2021-12-10T03:17:27","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/?post_type=chapter&#038;p=6632"},"modified":"2021-12-10T03:23:59","modified_gmt":"2021-12-10T03:23:59","slug":"2c-writing-and-naming-whole-and-decimal-numbers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/chapter\/2c-writing-and-naming-whole-and-decimal-numbers\/","title":{"raw":"2C Writing and Naming Whole and Decimal Numbers","rendered":"2C Writing and Naming Whole and Decimal Numbers"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Write a whole number given as digits in words<\/li>\r\n \t<li>Write a whole number given in words as digits<\/li>\r\n \t<li>Name a decimal number<\/li>\r\n \t<li>Given the name of a decimal number, write it in decimal notation<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Use Place Value to Name Whole Numbers<\/h2>\r\nWhen you write a check, you write out the number in words as well as in digits. To write a number in words, write the number in each period followed by the name of the period without the \u2018s\u2019 at the end. Start with the digit at the left, which has the largest place value. The commas separate the periods, so wherever there is a comma in the number, write a comma between the words. The ones period, which has the smallest place value, is not named.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215218\/CNX_BMath_Figure_01_01_013_img.png\" alt=\"An image with three values separated by commas. The first value is \" \/>\r\nSo the number [latex]37,519,248[\/latex] is written thirty-seven million, five hundred nineteen thousand, two hundred forty-eight.\r\nNotice that the word <em>and<\/em> is not used when naming a whole number.\r\n<div class=\"textbox shaded\">\r\n<h3 class=\"title\">Name a whole number in words<\/h3>\r\n<ol id=\"eip-375\" class=\"stepwise\">\r\n \t<li>Starting at the digit on the left, name the number in each period, followed by the period name. Do not include the period name for the ones.<\/li>\r\n \t<li>Use commas in the number to separate the periods.<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nName the number [latex]8,165,432,098,710[\/latex] in words.\r\n\r\nSolution\r\n<table id=\"fs-id1171100715908\" class=\"unnumbered unstyled\" summary=\"Begin with the leftmost digit, which is 8. It is in the trillions place. Eight trillion. \/ The next period to the right is billions - one hundred sixty-five billion. \/ The next period to the right is millions - four hundred thirty-two million. \/ The next period to the right is thousands - ninety-eight thousand. \/ The rightmost period shows the ones - seven hundred ten.\">\r\n<tbody>\r\n<tr>\r\n<td>Begin with the leftmost digit, which is[latex]8[\/latex]. It is in the trillions place.<\/td>\r\n<td>eight trillion<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The next period to the right is billions.<\/td>\r\n<td>one hundred sixty-five billion<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The next period to the right is millions.<\/td>\r\n<td>four hundred thirty-two million<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The next period to the right is thousands.<\/td>\r\n<td>ninety-eight thousand<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The rightmost period shows the ones.<\/td>\r\n<td>seven hundred ten<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215220\/CNX_BMath_Figure_01_01_014_img.png\" alt=\"An image with five values separated by commas. The first value is \" \/>\r\nPutting all of the words together, we write [latex]8,165,432,098,710[\/latex] as eight trillion, one hundred sixty-five billion, four hundred thirty-two million, ninety-eight thousand, seven hundred ten.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nA student conducted research and found that the number of mobile phone users in the United States during one month in [latex]2014[\/latex] was [latex]327,577,529[\/latex]. Name that number in words.\r\n[reveal-answer q=\"692742\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"692742\"]\r\nIdentify the periods associated with the number.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215222\/CNX_BMath_Figure_01_01_015_img.png\" alt=\"An image with three values separated by commas. The first value is \" \/>\r\n\r\nName the number in each period, followed by the period name. Put the commas in to separate the periods.\r\n\r\n<strong>Millions period<\/strong>: three hundred twenty-seven million\r\n<strong>Thousands period<\/strong>: five hundred seventy-seven thousand\r\n<strong>Ones period<\/strong>: five hundred twenty-nine\r\n\r\nSo the number of mobile phone users in the Unites States during the month of April was three hundred twenty-seven million, five hundred seventy-seven thousand, five hundred twenty-nine.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]143026[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<h2>Use Place Value to Write Whole Numbers<\/h2>\r\nWe will now reverse the process and write a number given in words as digits.\r\n<div class=\"textbox shaded\">\r\n<h3 class=\"title\">Use place value to write a whole number<\/h3>\r\n<ol id=\"eip-100\" class=\"stepwise\">\r\n \t<li>Identify the words that indicate periods. (Remember the ones period is never named.)<\/li>\r\n \t<li>Draw three blanks to indicate the number of places needed in each period. Separate the periods by commas.<\/li>\r\n \t<li>Name the number in each period and place the digits in the correct place value position.<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWrite the following numbers using digits.\r\n<ol>\r\n \t<li>fifty-three million, four hundred one thousand, seven hundred forty-two<\/li>\r\n \t<li>nine billion, two hundred forty-six million, seventy-three thousand, one hundred eighty-nine<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"605912\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"605912\"]\r\n1.\r\n<ul>\r\n \t<li>Identify the words that indicate periods.<\/li>\r\n \t<li>Except for the first period, all other periods must have three places.<\/li>\r\n \t<li>Draw three blanks to indicate the number of places needed in each period.<\/li>\r\n \t<li>Separate the periods by commas.<\/li>\r\n \t<li>Then write the digits in each period.<\/li>\r\n<\/ul>\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215223\/CNX_BMath_Figure_01_01_016_img.png\" alt=\"An image with three blocks of text pointing to numerical values. The first block of text is \" \/>\r\nPut the numbers together, including the commas. The number is [latex]53,401,742[\/latex].\r\n\r\n&nbsp;\r\n\r\n2.\r\n<ul>\r\n \t<li>Identify the words that indicate periods.<\/li>\r\n \t<li>Except for the first period, all other periods must have three places.<\/li>\r\n \t<li>Draw three blanks to indicate the number of places needed in each period.<\/li>\r\n \t<li>Separate the periods by commas.<\/li>\r\n \t<li>Then write the digits in each period.<\/li>\r\n<\/ul>\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215225\/CNX_BMath_Figure_01_01_017_img.png\" alt=\"An image with four blocks of text pointing to numerical values. The first block of text is \" \/>\r\nThe number is [latex]9,246,073,189[\/latex].\r\n\r\nNotice that in part (2), a zero was needed as a place-holder in the hundred thousands place. Be sure to write zeros as needed to make sure that each period, except possibly the first, has three places.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]143028[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nA state budget was about [latex]\\text{\\$77}[\/latex] billion. Write the budget in standard form.\r\n[reveal-answer q=\"595048\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"595048\"]\r\n\r\nIdentify the periods. In this case, only two digits are given and they are in the billions period. To write the entire number, write zeros for all of the other periods.\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215228\/CNX_BMath_Figure_01_01_018_img.png\" alt=\"An image with four blocks of text pointing to numerical values. The first block of text is \" \/>\r\nSo the budget was about [latex]\\text{\\$77,000,000,000.}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\nWrite each number in standard form:\r\n<ol>\r\n \t<li id=\"fs-id1800228\">The closest distance from Earth to Mars is about [latex]34[\/latex] million miles.<\/li>\r\n \t<li>The total weight of an aircraft carrier is [latex]204[\/latex] million pounds.<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"198073\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"198073\"]\r\n<ol>\r\n \t<li>[latex]34,000,000[\/latex] miles<\/li>\r\n \t<li>[latex]204,000,000[\/latex] pounds<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nThe video below shows more examples of how to use place value to write the name of a whole number.\r\n\r\nhttps:\/\/youtu.be\/H9HpkvY_iaE\r\n<h1>WRITING DECIMAL NUMBERS IN WORDS<\/h1>\r\nYou probably already know quite a bit about decimals based on your experience with money. Suppose you buy a sandwich and a bottle of water for lunch. If the sandwich costs [latex]\\text{\\$3.45}[\/latex] , the bottle of water costs [latex]\\text{\\$1.25}[\/latex] , and the total sales tax is [latex]\\text{\\$0.33}[\/latex] , what is the total cost of your lunch?\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221427\/CNX_BMath_Figure_05_01_002_img.png\" alt=\"A vertical addition problem is shown. The top line shows $3.45 for a sandwich, the next line shows $1.25 for water, and the last line shows $0.33 for tax. The total is shown to be $5.03.\" \/>\r\nThe total is [latex]$5.03[\/latex]. Suppose you pay with a [latex]$5[\/latex] bill and [latex]3[\/latex] pennies. Should you wait for change? No, [latex]\\text{\\$5}[\/latex] and [latex]3[\/latex] pennies is the same as [latex]\\text{\\$5.03}[\/latex].\r\n\r\nBecause [latex]\\text{100 pennies}=\\text{\\$1}[\/latex], each penny is worth [latex]{\\Large\\frac{1}{100}}[\/latex] of a dollar. We write the value of one penny as [latex]$0.01[\/latex], since [latex]0.01={\\Large\\frac{1}{100}}[\/latex].\r\n\r\nWriting a number with a decimal is known as decimal notation. It is a way of showing parts of a whole when the whole is a power of ten. In other words, decimals are another way of writing fractions whose denominators are powers of ten. Just as the counting numbers are based on powers of ten, decimals are based on powers of ten. The table below shows the counting numbers.\r\n<div class=\"textbox shaded\">\r\n<table id=\"fs-id1383547\" summary=\"A table is shown with two columns and six rows. The first row is a header row and it labels each column, \">\r\n<thead>\r\n<tr>\r\n<th>Counting number<\/th>\r\n<th>Name<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>One<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]10=10[\/latex]<\/td>\r\n<td>Ten<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]10\\cdot 10=100[\/latex]<\/td>\r\n<td>One hundred<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]10\\cdot 10\\cdot 10=1000[\/latex]<\/td>\r\n<td>One thousand<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]10\\cdot 10\\cdot 10\\cdot 10=10,000[\/latex]<\/td>\r\n<td>Ten thousand<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nHow are decimals related to fractions? The table below shows the relation.\r\n<div class=\"textbox shaded\">\r\n<table id=\"fs-id2474612\" summary=\"A table is shown with three columns and five rows. The first row is a header row and it labels each column, \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Decimal<\/th>\r\n<th>Fraction<\/th>\r\n<th>Name<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]0.1[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{1}{10}}[\/latex]<\/td>\r\n<td>One tenth<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]0.01[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{1}{100}}[\/latex]<\/td>\r\n<td>One hundredth<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]0.001[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{1}{1,000}}[\/latex]<\/td>\r\n<td>One thousandth<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]0.0001[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{1}{10,000}}[\/latex]<\/td>\r\n<td>One ten-thousandth<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nWhen we name a whole number, the name corresponds to the place value based on the powers of ten. In Whole Numbers, we learned to read [latex]10,000[\/latex] as <em>ten thousand<\/em>. Likewise, the names of the decimal places correspond to their fraction values. Notice how the place value names in the first table relate to the names of the fractions from the second table.\r\n\r\nThis chart illustrates place values to the left and right of the decimal point.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221429\/CNX_BMath_Figure_05_01_002.png\" alt=\"A chart is shown labeled \" \/>\r\nNotice two important facts shown in the tables.\r\n<ul id=\"fs-id1852418\">\r\n \t<li>The \"th\" at the end of the name means the number is a fraction. \"One thousand\" is a number larger than one, but \"one thousandth\" is a number smaller than one.<\/li>\r\n \t<li>The tenths place is the first place to the right of the decimal, but the tens place is two places to the left of the decimal.<\/li>\r\n<\/ul>\r\nRemember that [latex]$5.03[\/latex] lunch? We read [latex]$5.03[\/latex] as <em>five dollars and three cents<\/em>. Naming decimals (those that don\u2019t represent money) is done in a similar way. We read the number [latex]5.03[\/latex] as <em>five and three hundredths<\/em>.\r\nWe sometimes need to translate a number written in decimal notation into words. As shown in the image below, we write the amount on a check in both words and numbers.\r\n\r\nWhen we write a check, we write the amount as a decimal number as well as in words. The bank looks at the check to make sure both numbers match. This helps prevent errors.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221431\/CNX_BMath_Figure_05_01_003.png\" alt=\"An image of a check is shown. The check is made out to Jane Doe. It shows the number $152.65 and says in words, \" \/>\r\n<table id=\"eip-363\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Let\u2019s try naming a decimal, such as [latex]15.68[\/latex].<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We start by naming the number to the left of the decimal.<\/td>\r\n<td>fifteen______<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We use the word \"and\" to indicate the decimal point.<\/td>\r\n<td>fifteen and_____<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Then we name the number to the right of the decimal point as if it were a whole number.<\/td>\r\n<td>fifteen and sixty-eight_____<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Last, name the decimal place of the last digit.<\/td>\r\n<td>fifteen and sixty-eight hundredths<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe number [latex]15.68[\/latex] is read <em>fifteen and sixty-eight hundredths<\/em>.\r\n<div class=\"textbox shaded\">\r\n<h3>Name a decimal number.<\/h3>\r\n<ul id=\"eip-id1168467377447\">\r\n \t<li>Name the number to the left of the decimal point.<\/li>\r\n \t<li>Write \"and\" for the decimal point.<\/li>\r\n \t<li>Name the \"number\" part to the right of the decimal point as if it were a whole number.<\/li>\r\n \t<li>Name the decimal place of the last digit.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\nName each decimal:\r\n\r\n1. [latex]4.3[\/latex]\r\n\r\n2. [latex]2.45[\/latex]\r\n\r\n3. [latex]0.009[\/latex]\r\n\r\n4. [latex]-15.571[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168466143644\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]4.3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Name the number to the left of the decimal point.<\/td>\r\n<td>four_____<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write \"and\" for the decimal point.<\/td>\r\n<td>four and_____<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Name the number to the right of the decimal point as if it were a whole number.<\/td>\r\n<td>four and three_____<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Name the decimal place of the last digit.<\/td>\r\n<td>four and three tenths<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168469455604\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]2.45[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Name the number to the left of the decimal point.<\/td>\r\n<td>two_____<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write \"and\" for the decimal point.<\/td>\r\n<td>two and_____<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Name the number to the right of the decimal point as if it were a whole number.<\/td>\r\n<td>two and forty-five_____<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Name the decimal place of the last digit.<\/td>\r\n<td>two and forty-five hundredths<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168469507978\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>3.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]0.009[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Name the number to the left of the decimal point.<\/td>\r\n<td>Zero is the number to the left of the decimal; it is not included in the name.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Name the number to the right of the decimal point as if it were a whole number.<\/td>\r\n<td>nine_____<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Name the decimal place of the last digit.<\/td>\r\n<td>nine thousandths<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168469769355\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>4.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]-15.571[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Name the number to the left of the decimal point.<\/td>\r\n<td>negative fifteen<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write \"and\" for the decimal point.<\/td>\r\n<td>negative fifteen and_____<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Name the number to the right of the decimal point as if it were a whole number.<\/td>\r\n<td>negative fifteen and five hundred seventy-one_____<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Name the decimal place of the last digit.<\/td>\r\n<td>negative fifteen and five hundred seventy-one thousandths<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY It<\/h3>\r\n[ohm_question]146224[\/ohm_question]\r\n\r\n[ohm_question]146225[\/ohm_question]\r\n\r\n[ohm_question]146568[\/ohm_question]\r\n\r\n[ohm_question]146569[\/ohm_question]\r\n\r\n<\/div>\r\nNow we will translate the name of a decimal number into decimal notation. We will reverse the procedure we just used.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\n1. Write the number six and seventeen hundredths:\r\n<table id=\"eip-id1168469639112\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>six and seventeen hundredths<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The word <em>and<\/em> tells us to place a decimal point.<\/td>\r\n<td>___.___<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The word before <em>and<\/em> is the whole number; write it to the left of the decimal point.<\/td>\r\n<td>[latex]6[\/latex]._____<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The decimal part is seventeen hundredths.\r\n\r\nMark two places to the right of the decimal point for hundredths.<\/td>\r\n<td>[latex]6[\/latex]._ _<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the numerals for seventeen in the places marked.<\/td>\r\n<td>[latex]6.17[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n2. Write fourteen and thirty-seven hundredths as a decimal.\r\n[reveal-answer q=\"796510\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"796510\"]\r\n\r\nSolution\r\n<table id=\"eip-569\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>fourteen and thirty-seven hundredths<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Place a decimal point under the word \u2018and\u2019.<\/td>\r\n<td>______. _________<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate the words before \u2018and\u2019 into the whole number and place it to the left of the decimal point.<\/td>\r\n<td>[latex]14[\/latex]. _________<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Mark two places to the right of the decimal point for \"hundredths\".<\/td>\r\n<td>[latex]14[\/latex].__ __<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate the words after \"and\" and write the number to the right of the decimal point.<\/td>\r\n<td>[latex]14.37[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Fourteen and thirty-seven hundredths is written [latex]14.37[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146570[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show more examples of how to write the name of a decimal using a place value chart.\r\n\r\nhttps:\/\/youtu.be\/aLsWWl2-aNE\r\n<div class=\"textbox shaded\">\r\n<h3>Write a decimal number from its name.<\/h3>\r\n<ol id=\"eip-id1168468315974\" class=\"stepwise\">\r\n \t<li>Look for the word \"and\"\u2014it locates the decimal point.<\/li>\r\n \t<li>Mark the number of decimal places needed to the right of the decimal point by noting the place value indicated by the last word.\r\n<ul id=\"eip-id1168468368974\">\r\n \t<li>Place a decimal point under the word \"and.\" Translate the words before \"and\" into the whole number and place it to the left of the decimal point.<\/li>\r\n \t<li>If there is no \"and,\" write a \"0\" with a decimal point to its right.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Translate the words after \"and\" into the number to the right of the decimal point. Write the number in the spaces\u2014putting the final digit in the last place.<\/li>\r\n \t<li>Fill in zeros for place holders as needed.<\/li>\r\n<\/ol>\r\n<\/div>\r\nThe second bullet in Step 1 is needed for decimals that have no whole number part, like \u2018nine thousandths\u2019. We recognize them by the words that indicate the place value after the decimal \u2013 such as \u2018tenths\u2019 or \u2018hundredths.\u2019 Since there is no whole number, there is no \u2018and.\u2019 We start by placing a zero to the left of the decimal and continue by filling in the numbers to the right, as we did above.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWrite twenty-four thousandths as a decimal.\r\n[reveal-answer q=\"425300\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"425300\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168466165707\" class=\"unnumbered unstyled\" summary=\"The first line says, \">\r\n<tbody>\r\n<tr>\r\n<td>twenty-four thousandths<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Look for the word \"and\".<\/td>\r\n<td>There is no \"and\" so start with 0\r\n\r\n[latex]0[\/latex].<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>To the right of the decimal point, put three decimal places for thousandths.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221434\/CNX_BMath_Figure_05_01_020_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the number [latex]24[\/latex] with the [latex]4[\/latex] in the thousandths place.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221435\/CNX_BMath_Figure_05_01_020_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Put zeros as placeholders in the remaining decimal places.<\/td>\r\n<td>[latex]0.024[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>So, twenty-four thousandths is written [latex]0.024[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146571[\/ohm_question]\r\n\r\n[ohm_question]146572[\/ohm_question]\r\n\r\n<\/div>\r\nIn the next video we will show more examples of how to write a decimal given its name in words.\r\n\r\nBefore we move on to our next objective, think about money again. We know that [latex]$1[\/latex] is the same as [latex]$1.00[\/latex]. The way we write [latex]$1\\left(\\text{or}$1.00\\right)[\/latex] depends on the context. In the same way, integers can be written as decimals with as many zeros as needed to the right of the decimal.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{cccc}5=5.0\\hfill &amp; &amp; &amp; -2=-2.0\\hfill \\\\ 5=5.00\\hfill &amp; &amp; &amp; -2=-2.00\\hfill \\\\ 5=5.000\\hfill &amp; &amp; &amp; -2=-2.000\\hfill \\end{array}[\/latex]\r\nand so on [latex]\\dots[\/latex]<\/p>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Write a whole number given as digits in words<\/li>\n<li>Write a whole number given in words as digits<\/li>\n<li>Name a decimal number<\/li>\n<li>Given the name of a decimal number, write it in decimal notation<\/li>\n<\/ul>\n<\/div>\n<h2>Use Place Value to Name Whole Numbers<\/h2>\n<p>When you write a check, you write out the number in words as well as in digits. To write a number in words, write the number in each period followed by the name of the period without the \u2018s\u2019 at the end. Start with the digit at the left, which has the largest place value. The commas separate the periods, so wherever there is a comma in the number, write a comma between the words. The ones period, which has the smallest place value, is not named.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215218\/CNX_BMath_Figure_01_01_013_img.png\" alt=\"An image with three values separated by commas. The first value is\" \/><br \/>\nSo the number [latex]37,519,248[\/latex] is written thirty-seven million, five hundred nineteen thousand, two hundred forty-eight.<br \/>\nNotice that the word <em>and<\/em> is not used when naming a whole number.<\/p>\n<div class=\"textbox shaded\">\n<h3 class=\"title\">Name a whole number in words<\/h3>\n<ol id=\"eip-375\" class=\"stepwise\">\n<li>Starting at the digit on the left, name the number in each period, followed by the period name. Do not include the period name for the ones.<\/li>\n<li>Use commas in the number to separate the periods.<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Name the number [latex]8,165,432,098,710[\/latex] in words.<\/p>\n<p>Solution<\/p>\n<table id=\"fs-id1171100715908\" class=\"unnumbered unstyled\" summary=\"Begin with the leftmost digit, which is 8. It is in the trillions place. Eight trillion. \/ The next period to the right is billions - one hundred sixty-five billion. \/ The next period to the right is millions - four hundred thirty-two million. \/ The next period to the right is thousands - ninety-eight thousand. \/ The rightmost period shows the ones - seven hundred ten.\">\n<tbody>\n<tr>\n<td>Begin with the leftmost digit, which is[latex]8[\/latex]. It is in the trillions place.<\/td>\n<td>eight trillion<\/td>\n<\/tr>\n<tr>\n<td>The next period to the right is billions.<\/td>\n<td>one hundred sixty-five billion<\/td>\n<\/tr>\n<tr>\n<td>The next period to the right is millions.<\/td>\n<td>four hundred thirty-two million<\/td>\n<\/tr>\n<tr>\n<td>The next period to the right is thousands.<\/td>\n<td>ninety-eight thousand<\/td>\n<\/tr>\n<tr>\n<td>The rightmost period shows the ones.<\/td>\n<td>seven hundred ten<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215220\/CNX_BMath_Figure_01_01_014_img.png\" alt=\"An image with five values separated by commas. The first value is\" \/><br \/>\nPutting all of the words together, we write [latex]8,165,432,098,710[\/latex] as eight trillion, one hundred sixty-five billion, four hundred thirty-two million, ninety-eight thousand, seven hundred ten.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>A student conducted research and found that the number of mobile phone users in the United States during one month in [latex]2014[\/latex] was [latex]327,577,529[\/latex]. Name that number in words.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q692742\">Show Solution<\/span><\/p>\n<div id=\"q692742\" class=\"hidden-answer\" style=\"display: none\">\nIdentify the periods associated with the number.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215222\/CNX_BMath_Figure_01_01_015_img.png\" alt=\"An image with three values separated by commas. The first value is\" \/><\/p>\n<p>Name the number in each period, followed by the period name. Put the commas in to separate the periods.<\/p>\n<p><strong>Millions period<\/strong>: three hundred twenty-seven million<br \/>\n<strong>Thousands period<\/strong>: five hundred seventy-seven thousand<br \/>\n<strong>Ones period<\/strong>: five hundred twenty-nine<\/p>\n<p>So the number of mobile phone users in the Unites States during the month of April was three hundred twenty-seven million, five hundred seventy-seven thousand, five hundred twenty-nine.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm143026\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143026&theme=oea&iframe_resize_id=ohm143026&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<h2>Use Place Value to Write Whole Numbers<\/h2>\n<p>We will now reverse the process and write a number given in words as digits.<\/p>\n<div class=\"textbox shaded\">\n<h3 class=\"title\">Use place value to write a whole number<\/h3>\n<ol id=\"eip-100\" class=\"stepwise\">\n<li>Identify the words that indicate periods. (Remember the ones period is never named.)<\/li>\n<li>Draw three blanks to indicate the number of places needed in each period. Separate the periods by commas.<\/li>\n<li>Name the number in each period and place the digits in the correct place value position.<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Write the following numbers using digits.<\/p>\n<ol>\n<li>fifty-three million, four hundred one thousand, seven hundred forty-two<\/li>\n<li>nine billion, two hundred forty-six million, seventy-three thousand, one hundred eighty-nine<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q605912\">Show Solution<\/span><\/p>\n<div id=\"q605912\" class=\"hidden-answer\" style=\"display: none\">\n1.<\/p>\n<ul>\n<li>Identify the words that indicate periods.<\/li>\n<li>Except for the first period, all other periods must have three places.<\/li>\n<li>Draw three blanks to indicate the number of places needed in each period.<\/li>\n<li>Separate the periods by commas.<\/li>\n<li>Then write the digits in each period.<\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215223\/CNX_BMath_Figure_01_01_016_img.png\" alt=\"An image with three blocks of text pointing to numerical values. The first block of text is\" \/><br \/>\nPut the numbers together, including the commas. The number is [latex]53,401,742[\/latex].<\/p>\n<p>&nbsp;<\/p>\n<p>2.<\/p>\n<ul>\n<li>Identify the words that indicate periods.<\/li>\n<li>Except for the first period, all other periods must have three places.<\/li>\n<li>Draw three blanks to indicate the number of places needed in each period.<\/li>\n<li>Separate the periods by commas.<\/li>\n<li>Then write the digits in each period.<\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215225\/CNX_BMath_Figure_01_01_017_img.png\" alt=\"An image with four blocks of text pointing to numerical values. The first block of text is\" \/><br \/>\nThe number is [latex]9,246,073,189[\/latex].<\/p>\n<p>Notice that in part (2), a zero was needed as a place-holder in the hundred thousands place. Be sure to write zeros as needed to make sure that each period, except possibly the first, has three places.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm143028\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143028&theme=oea&iframe_resize_id=ohm143028&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>A state budget was about [latex]\\text{\\$77}[\/latex] billion. Write the budget in standard form.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q595048\">Show Solution<\/span><\/p>\n<div id=\"q595048\" class=\"hidden-answer\" style=\"display: none\">\n<p>Identify the periods. In this case, only two digits are given and they are in the billions period. To write the entire number, write zeros for all of the other periods.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215228\/CNX_BMath_Figure_01_01_018_img.png\" alt=\"An image with four blocks of text pointing to numerical values. The first block of text is\" \/><br \/>\nSo the budget was about [latex]\\text{\\$77,000,000,000.}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p>Write each number in standard form:<\/p>\n<ol>\n<li id=\"fs-id1800228\">The closest distance from Earth to Mars is about [latex]34[\/latex] million miles.<\/li>\n<li>The total weight of an aircraft carrier is [latex]204[\/latex] million pounds.<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q198073\">Show Solution<\/span><\/p>\n<div id=\"q198073\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>[latex]34,000,000[\/latex] miles<\/li>\n<li>[latex]204,000,000[\/latex] pounds<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>The video below shows more examples of how to use place value to write the name of a whole number.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Example:  Write a Whole Number in Digits from Words\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/H9HpkvY_iaE?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h1>WRITING DECIMAL NUMBERS IN WORDS<\/h1>\n<p>You probably already know quite a bit about decimals based on your experience with money. Suppose you buy a sandwich and a bottle of water for lunch. If the sandwich costs [latex]\\text{\\$3.45}[\/latex] , the bottle of water costs [latex]\\text{\\$1.25}[\/latex] , and the total sales tax is [latex]\\text{\\$0.33}[\/latex] , what is the total cost of your lunch?<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221427\/CNX_BMath_Figure_05_01_002_img.png\" alt=\"A vertical addition problem is shown. The top line shows $3.45 for a sandwich, the next line shows $1.25 for water, and the last line shows $0.33 for tax. The total is shown to be $5.03.\" \/><br \/>\nThe total is [latex]$5.03[\/latex]. Suppose you pay with a [latex]$5[\/latex] bill and [latex]3[\/latex] pennies. Should you wait for change? No, [latex]\\text{\\$5}[\/latex] and [latex]3[\/latex] pennies is the same as [latex]\\text{\\$5.03}[\/latex].<\/p>\n<p>Because [latex]\\text{100 pennies}=\\text{\\$1}[\/latex], each penny is worth [latex]{\\Large\\frac{1}{100}}[\/latex] of a dollar. We write the value of one penny as [latex]$0.01[\/latex], since [latex]0.01={\\Large\\frac{1}{100}}[\/latex].<\/p>\n<p>Writing a number with a decimal is known as decimal notation. It is a way of showing parts of a whole when the whole is a power of ten. In other words, decimals are another way of writing fractions whose denominators are powers of ten. Just as the counting numbers are based on powers of ten, decimals are based on powers of ten. The table below shows the counting numbers.<\/p>\n<div class=\"textbox shaded\">\n<table id=\"fs-id1383547\" summary=\"A table is shown with two columns and six rows. The first row is a header row and it labels each column,\">\n<thead>\n<tr>\n<th>Counting number<\/th>\n<th>Name<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]1[\/latex]<\/td>\n<td>One<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]10=10[\/latex]<\/td>\n<td>Ten<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]10\\cdot 10=100[\/latex]<\/td>\n<td>One hundred<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]10\\cdot 10\\cdot 10=1000[\/latex]<\/td>\n<td>One thousand<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]10\\cdot 10\\cdot 10\\cdot 10=10,000[\/latex]<\/td>\n<td>Ten thousand<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>How are decimals related to fractions? The table below shows the relation.<\/p>\n<div class=\"textbox shaded\">\n<table id=\"fs-id2474612\" summary=\"A table is shown with three columns and five rows. The first row is a header row and it labels each column,\">\n<thead>\n<tr valign=\"top\">\n<th>Decimal<\/th>\n<th>Fraction<\/th>\n<th>Name<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]0.1[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{1}{10}}[\/latex]<\/td>\n<td>One tenth<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]0.01[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{1}{100}}[\/latex]<\/td>\n<td>One hundredth<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]0.001[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{1}{1,000}}[\/latex]<\/td>\n<td>One thousandth<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]0.0001[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{1}{10,000}}[\/latex]<\/td>\n<td>One ten-thousandth<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>When we name a whole number, the name corresponds to the place value based on the powers of ten. In Whole Numbers, we learned to read [latex]10,000[\/latex] as <em>ten thousand<\/em>. Likewise, the names of the decimal places correspond to their fraction values. Notice how the place value names in the first table relate to the names of the fractions from the second table.<\/p>\n<p>This chart illustrates place values to the left and right of the decimal point.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221429\/CNX_BMath_Figure_05_01_002.png\" alt=\"A chart is shown labeled\" \/><br \/>\nNotice two important facts shown in the tables.<\/p>\n<ul id=\"fs-id1852418\">\n<li>The &#8220;th&#8221; at the end of the name means the number is a fraction. &#8220;One thousand&#8221; is a number larger than one, but &#8220;one thousandth&#8221; is a number smaller than one.<\/li>\n<li>The tenths place is the first place to the right of the decimal, but the tens place is two places to the left of the decimal.<\/li>\n<\/ul>\n<p>Remember that [latex]$5.03[\/latex] lunch? We read [latex]$5.03[\/latex] as <em>five dollars and three cents<\/em>. Naming decimals (those that don\u2019t represent money) is done in a similar way. We read the number [latex]5.03[\/latex] as <em>five and three hundredths<\/em>.<br \/>\nWe sometimes need to translate a number written in decimal notation into words. As shown in the image below, we write the amount on a check in both words and numbers.<\/p>\n<p>When we write a check, we write the amount as a decimal number as well as in words. The bank looks at the check to make sure both numbers match. This helps prevent errors.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221431\/CNX_BMath_Figure_05_01_003.png\" alt=\"An image of a check is shown. The check is made out to Jane Doe. It shows the number $152.65 and says in words,\" \/><\/p>\n<table id=\"eip-363\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Let\u2019s try naming a decimal, such as [latex]15.68[\/latex].<\/td>\n<\/tr>\n<tr>\n<td>We start by naming the number to the left of the decimal.<\/td>\n<td>fifteen______<\/td>\n<\/tr>\n<tr>\n<td>We use the word &#8220;and&#8221; to indicate the decimal point.<\/td>\n<td>fifteen and_____<\/td>\n<\/tr>\n<tr>\n<td>Then we name the number to the right of the decimal point as if it were a whole number.<\/td>\n<td>fifteen and sixty-eight_____<\/td>\n<\/tr>\n<tr>\n<td>Last, name the decimal place of the last digit.<\/td>\n<td>fifteen and sixty-eight hundredths<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The number [latex]15.68[\/latex] is read <em>fifteen and sixty-eight hundredths<\/em>.<\/p>\n<div class=\"textbox shaded\">\n<h3>Name a decimal number.<\/h3>\n<ul id=\"eip-id1168467377447\">\n<li>Name the number to the left of the decimal point.<\/li>\n<li>Write &#8220;and&#8221; for the decimal point.<\/li>\n<li>Name the &#8220;number&#8221; part to the right of the decimal point as if it were a whole number.<\/li>\n<li>Name the decimal place of the last digit.<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>Name each decimal:<\/p>\n<p>1. [latex]4.3[\/latex]<\/p>\n<p>2. [latex]2.45[\/latex]<\/p>\n<p>3. [latex]0.009[\/latex]<\/p>\n<p>4. [latex]-15.571[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168466143644\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<\/tr>\n<tr>\n<td>[latex]4.3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Name the number to the left of the decimal point.<\/td>\n<td>four_____<\/td>\n<\/tr>\n<tr>\n<td>Write &#8220;and&#8221; for the decimal point.<\/td>\n<td>four and_____<\/td>\n<\/tr>\n<tr>\n<td>Name the number to the right of the decimal point as if it were a whole number.<\/td>\n<td>four and three_____<\/td>\n<\/tr>\n<tr>\n<td>Name the decimal place of the last digit.<\/td>\n<td>four and three tenths<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469455604\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<\/tr>\n<tr>\n<td>[latex]2.45[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Name the number to the left of the decimal point.<\/td>\n<td>two_____<\/td>\n<\/tr>\n<tr>\n<td>Write &#8220;and&#8221; for the decimal point.<\/td>\n<td>two and_____<\/td>\n<\/tr>\n<tr>\n<td>Name the number to the right of the decimal point as if it were a whole number.<\/td>\n<td>two and forty-five_____<\/td>\n<\/tr>\n<tr>\n<td>Name the decimal place of the last digit.<\/td>\n<td>two and forty-five hundredths<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469507978\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>3.<\/td>\n<\/tr>\n<tr>\n<td>[latex]0.009[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Name the number to the left of the decimal point.<\/td>\n<td>Zero is the number to the left of the decimal; it is not included in the name.<\/td>\n<\/tr>\n<tr>\n<td>Name the number to the right of the decimal point as if it were a whole number.<\/td>\n<td>nine_____<\/td>\n<\/tr>\n<tr>\n<td>Name the decimal place of the last digit.<\/td>\n<td>nine thousandths<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469769355\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>4.<\/td>\n<\/tr>\n<tr>\n<td>[latex]-15.571[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Name the number to the left of the decimal point.<\/td>\n<td>negative fifteen<\/td>\n<\/tr>\n<tr>\n<td>Write &#8220;and&#8221; for the decimal point.<\/td>\n<td>negative fifteen and_____<\/td>\n<\/tr>\n<tr>\n<td>Name the number to the right of the decimal point as if it were a whole number.<\/td>\n<td>negative fifteen and five hundred seventy-one_____<\/td>\n<\/tr>\n<tr>\n<td>Name the decimal place of the last digit.<\/td>\n<td>negative fifteen and five hundred seventy-one thousandths<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146224\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146224&theme=oea&iframe_resize_id=ohm146224&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146225\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146225&theme=oea&iframe_resize_id=ohm146225&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146568\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146568&theme=oea&iframe_resize_id=ohm146568&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146569\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146569&theme=oea&iframe_resize_id=ohm146569&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Now we will translate the name of a decimal number into decimal notation. We will reverse the procedure we just used.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>1. Write the number six and seventeen hundredths:<\/p>\n<table id=\"eip-id1168469639112\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>six and seventeen hundredths<\/td>\n<\/tr>\n<tr>\n<td>The word <em>and<\/em> tells us to place a decimal point.<\/td>\n<td>___.___<\/td>\n<\/tr>\n<tr>\n<td>The word before <em>and<\/em> is the whole number; write it to the left of the decimal point.<\/td>\n<td>[latex]6[\/latex]._____<\/td>\n<\/tr>\n<tr>\n<td>The decimal part is seventeen hundredths.<\/p>\n<p>Mark two places to the right of the decimal point for hundredths.<\/td>\n<td>[latex]6[\/latex]._ _<\/td>\n<\/tr>\n<tr>\n<td>Write the numerals for seventeen in the places marked.<\/td>\n<td>[latex]6.17[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>2. Write fourteen and thirty-seven hundredths as a decimal.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q796510\">Show Solution<\/span><\/p>\n<div id=\"q796510\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-569\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>fourteen and thirty-seven hundredths<\/td>\n<\/tr>\n<tr>\n<td>Place a decimal point under the word \u2018and\u2019.<\/td>\n<td>______. _________<\/td>\n<\/tr>\n<tr>\n<td>Translate the words before \u2018and\u2019 into the whole number and place it to the left of the decimal point.<\/td>\n<td>[latex]14[\/latex]. _________<\/td>\n<\/tr>\n<tr>\n<td>Mark two places to the right of the decimal point for &#8220;hundredths&#8221;.<\/td>\n<td>[latex]14[\/latex].__ __<\/td>\n<\/tr>\n<tr>\n<td>Translate the words after &#8220;and&#8221; and write the number to the right of the decimal point.<\/td>\n<td>[latex]14.37[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Fourteen and thirty-seven hundredths is written [latex]14.37[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146570\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146570&theme=oea&iframe_resize_id=ohm146570&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show more examples of how to write the name of a decimal using a place value chart.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Read and Write Decimals\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/aLsWWl2-aNE?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox shaded\">\n<h3>Write a decimal number from its name.<\/h3>\n<ol id=\"eip-id1168468315974\" class=\"stepwise\">\n<li>Look for the word &#8220;and&#8221;\u2014it locates the decimal point.<\/li>\n<li>Mark the number of decimal places needed to the right of the decimal point by noting the place value indicated by the last word.\n<ul id=\"eip-id1168468368974\">\n<li>Place a decimal point under the word &#8220;and.&#8221; Translate the words before &#8220;and&#8221; into the whole number and place it to the left of the decimal point.<\/li>\n<li>If there is no &#8220;and,&#8221; write a &#8220;0&#8221; with a decimal point to its right.<\/li>\n<\/ul>\n<\/li>\n<li>Translate the words after &#8220;and&#8221; into the number to the right of the decimal point. Write the number in the spaces\u2014putting the final digit in the last place.<\/li>\n<li>Fill in zeros for place holders as needed.<\/li>\n<\/ol>\n<\/div>\n<p>The second bullet in Step 1 is needed for decimals that have no whole number part, like \u2018nine thousandths\u2019. We recognize them by the words that indicate the place value after the decimal \u2013 such as \u2018tenths\u2019 or \u2018hundredths.\u2019 Since there is no whole number, there is no \u2018and.\u2019 We start by placing a zero to the left of the decimal and continue by filling in the numbers to the right, as we did above.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Write twenty-four thousandths as a decimal.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q425300\">Show Solution<\/span><\/p>\n<div id=\"q425300\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168466165707\" class=\"unnumbered unstyled\" summary=\"The first line says,\">\n<tbody>\n<tr>\n<td>twenty-four thousandths<\/td>\n<\/tr>\n<tr>\n<td>Look for the word &#8220;and&#8221;.<\/td>\n<td>There is no &#8220;and&#8221; so start with 0<\/p>\n<p>[latex]0[\/latex].<\/td>\n<\/tr>\n<tr>\n<td>To the right of the decimal point, put three decimal places for thousandths.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221434\/CNX_BMath_Figure_05_01_020_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write the number [latex]24[\/latex] with the [latex]4[\/latex] in the thousandths place.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221435\/CNX_BMath_Figure_05_01_020_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Put zeros as placeholders in the remaining decimal places.<\/td>\n<td>[latex]0.024[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>So, twenty-four thousandths is written [latex]0.024[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146571\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146571&theme=oea&iframe_resize_id=ohm146571&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146572\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146572&theme=oea&iframe_resize_id=ohm146572&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the next video we will show more examples of how to write a decimal given its name in words.<\/p>\n<p>Before we move on to our next objective, think about money again. We know that [latex]$1[\/latex] is the same as [latex]$1.00[\/latex]. The way we write [latex]$1\\left(\\text{or}$1.00\\right)[\/latex] depends on the context. In the same way, integers can be written as decimals with as many zeros as needed to the right of the decimal.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{cccc}5=5.0\\hfill & & & -2=-2.0\\hfill \\\\ 5=5.00\\hfill & & & -2=-2.00\\hfill \\\\ 5=5.000\\hfill & & & -2=-2.000\\hfill \\end{array}[\/latex]<br \/>\nand so on [latex]\\dots[\/latex]<\/p>\n","protected":false},"author":359705,"menu_order":3,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-6632","chapter","type-chapter","status-publish","hentry"],"part":6629,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/6632","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/users\/359705"}],"version-history":[{"count":5,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/6632\/revisions"}],"predecessor-version":[{"id":6637,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/6632\/revisions\/6637"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/parts\/6629"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapters\/6632\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/media?parent=6632"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/pressbooks\/v2\/chapter-type?post=6632"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/contributor?post=6632"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/frontrange-mathforliberalartscorequisite1\/wp-json\/wp\/v2\/license?post=6632"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}