{"id":15323,"date":"2021-10-11T23:05:30","date_gmt":"2021-10-11T23:05:30","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/converting-between-u-s-and-metric-systems-of-measurement\/"},"modified":"2021-10-27T03:30:51","modified_gmt":"2021-10-27T03:30:51","slug":"converting-between-u-s-and-metric-systems-of-measurement","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/converting-between-u-s-and-metric-systems-of-measurement\/","title":{"raw":"Converting Between U.S. and Metric Systems of Measurement","rendered":"Converting Between U.S. and Metric Systems of Measurement"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Convert between the U.S. and the metric systems of measurement<\/li>\r\n \t<li>Convert between Fahrenheit and Celsius temperatures<\/li>\r\n<\/ul>\r\n<\/div>\r\nMany measurements in the United States are made in metric units. A drink may come in [latex]\\text{2-liter}[\/latex] bottles, calcium may come in [latex]\\text{500-mg}[\/latex] capsules, and we may run a [latex]\\text{5-K}[\/latex] race. To work easily in both systems, we need to be able to convert between the two systems.\r\n\r\nThe reference table below shows some of the most common conversions.\r\n<table id=\"fs-id1412303\" summary=\"The table is labeled in the first row as \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th colspan=\"3\">Conversion Factors Between U.S. and Metric Systems<\/th>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<th>Length<\/th>\r\n<th>Weight<\/th>\r\n<th>Volume<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]1[\/latex] in = [latex]2.54[\/latex] cm\r\n\r\n[latex]1[\/latex] ft = [latex]0.305[\/latex] m\r\n\r\n[latex]1[\/latex] yd = [latex]0.914[\/latex] m\r\n\r\n[latex]1[\/latex] mi = [latex]1.61[\/latex] km\r\n\r\n[latex]1[\/latex] m = [latex]3.28[\/latex] ft<\/td>\r\n<td>[latex]1[\/latex] lb = [latex]0.45[\/latex] kg\r\n\r\n[latex]1[\/latex] oz = [latex]28[\/latex] g\r\n\r\n[latex]1[\/latex] kg = [latex]2.2[\/latex] lb<\/td>\r\n<td>[latex]1[\/latex] qt = [latex]0.95[\/latex] L\r\n\r\n[latex]1[\/latex] fl oz = [latex]30[\/latex] mL\r\n\r\n[latex]1[\/latex] L = [latex]1.06[\/latex] qt<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWe make conversions between the systems just as we do within the systems\u2014by multiplying by unit conversion factors.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nLee\u2019s water bottle holds [latex]500[\/latex] mL of water. How many fluid ounces are in the bottle? Round to the nearest tenth of an ounce.\r\n\r\nSolution\r\n<table id=\"eip-id1168466006710\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]500\\text{mL}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply by a unit conversion factor relating mL and ounces.<\/td>\r\n<td>[latex]500\\text{mL}\\cdot\\Large\\frac{1\\text{fl oz}}{30\\text{mL}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]\\Large\\frac{500\\text{fl oz}}{30}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide.<\/td>\r\n<td>[latex]16.7\\text{fl. oz.}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>The water bottle holds [latex]16.7[\/latex] fluid ounces.<\/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]146876[\/ohm_question]\r\n\r\n[ohm_question]146877[\/ohm_question]\r\n\r\n<\/div>\r\nThe conversion factors in the reference table\u00a0are not exact, but the approximations they give are close enough for everyday purposes. In the last example, we rounded the number of fluid ounces to the nearest tenth.\r\n<div class=\"textbox exercises\">\r\n<h3>ExERCISE<\/h3>\r\nSoleil lives in Minnesota but often travels in Canada for work. While driving on a Canadian highway, she passes a sign that says the next rest stop is in [latex]100[\/latex] kilometers. How many miles until the next rest stop? Round your answer to the nearest mile.\r\n[reveal-answer q=\"462849\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"462849\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468500910\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\text{100 kilometers}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply by a unit conversion factor relating kilometers and miles.<\/td>\r\n<td>[latex]100\\text{kilometers}\\cdot\r\n\r\n\\Large\\frac{1\\text{mile}}{1.61\\text{kilometers}}[\/latex]\r\n\r\n[latex]100\\cdot\r\n\r\n\\Large\\frac{1\\text{mi}}{1.61\\text{km}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]\\Large\\frac{100\\text{mi}}{1.61}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide.<\/td>\r\n<td>[latex]62 \\text{mi}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>It is about [latex]62[\/latex] miles to the next rest stop.<\/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\u00a0IT<\/h3>\r\n[ohm_question]146878[\/ohm_question]\r\n\r\n[ohm_question]146879[\/ohm_question]\r\n\r\n<\/div>\r\n<h3>Convert Between Fahrenheit and Celsius Temperatures<\/h3>\r\nHave you ever been in a foreign country and heard the weather forecast? If the forecast is for [latex]22^\\circ C[\/latex]. What does that mean?\r\n\r\nThe U.S. and metric systems use different scales to measure temperature. The U.S. system uses degrees Fahrenheit, written [latex]^\\circ F[\/latex]. The metric system uses degrees Celsius, written [latex]^\\circ C[\/latex]. The image below\u00a0shows the relationship between the two systems.\r\n\r\nA temperature of [latex]37^\\circ C[\/latex] is equivalent to [latex]98.6^\\circ F[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222516\/CNX_BMath_Figure_07_05_018.png\" alt=\"On the left side of the figure is a thermometer marked in degrees Celsius. The bottom of the thermometer begins with negative 20 degrees Celsius and ranges up to 100 degrees Celsius. There are tick marks on the thermometer every 5 degrees with every 10 degrees labeled. On the right side is a thermometer marked in degrees Fahrenheit. The bottom of the thermometer begins with negative 10 degrees Fahrenheit and ranges up to 212 degrees Fahrenheit. There are tick marks on the thermometer every 2 degrees with every 10 degrees labeled. Between the thermometers there is an arrow pointing on the left to 0 degrees Celsius and on the right to 32 degrees Fahrenheit. This is the temperature at which water freezes. Another arrow points on the left to 37 degrees Celsius and on the right to 98.6 degrees Fahrenheit. This is normal body temperature. A third arrow points on the left to 100 degrees Celsius and on the right to 212 degrees Fahrenheit. This is the temperature at which water boils.\" \/>\r\nIf we know the temperature in one system, we can use a formula to convert it to the other system.\r\n<div class=\"textbox shaded\">\r\n<h3>Temperature Conversion<\/h3>\r\nTo convert from Fahrenheit temperature, [latex]\\text{F}[\/latex], to Celsius temperature, [latex]\\text{C}[\/latex], use the formula\r\n\r\n[latex]C=\\Large\\frac{5}{9}\\normalsize\\left(F - 32\\right)[\/latex]\r\nTo convert from Celsius temperature, [latex]\\text{C}[\/latex], to Fahrenheit temperature, [latex]\\text{F}[\/latex], use the formula\r\n\r\n[latex]F=\\Large\\frac{9}{5}\\normalsize C+32[\/latex]\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Example:\u00a0<strong>Conversion from Celsius<\/strong><\/h3>\r\nNormal body temperature has been commonly accepted as 37.0 \u00b0C (although it varies depending on time of day and method of measurement, as well as among individuals). What is this temperature on the kelvin scale and on the Fahrenheit scale?\r\n\r\n[reveal-answer q=\"478867\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"478867\"]\r\n<p style=\"text-align: center;\">[latex]\\text{K}=\\text{ }^{\\circ}\\text{C}+273.15=37.0+273.2=\\text{310.2 K}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\text{ }^{\\circ}\\text{F}=\\frac{9}{5}^{\\circ}\\text{ C}+32.0=\\left(\\frac{9}{5}\\times 37.0\\right)+32.0=66.6+32.0=98.6^{\\circ}\\text{ F}[\/latex]<\/p>\r\n[\/hidden-answer]\r\n<h4>Check Your Learning<\/h4>\r\nConvert 80.92 \u00b0C to K and \u00b0F.\r\n\r\n[reveal-answer q=\"753412\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"753412\"]354.07 K, 177.7 \u00b0F[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Example:\u00a0<strong>Conversion from Fahrenheit<\/strong><\/h3>\r\nBaking a ready-made pizza calls for an oven temperature of 450 \u00b0F. If you are in Europe, and your oven thermometer uses the Celsius scale, what is the setting? What is the kelvin temperature?\r\n\r\n[reveal-answer q=\"43910\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"43910\"]\r\n<p style=\"text-align: center;\">[latex]\\text{ }^{\\circ}\\text{C}=\\frac{5}{9}(^{\\circ}\\text{ F}-\\text{32)}=\\frac{5}{9}\\left(450-32\\right)=\\frac{5}{9}\\times 418=232^{\\circ}\\text{ C}\\rightarrow\\text{set oven to 230}^{\\circ}\\text{ C}\\left(\\text{two significant figures}\\right)[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\text{K}=\\text{ }^{\\circ}\\text{ C}+273.15=230+273=\\text{503 K}\\rightarrow 5.0\\times {10}^{2}\\text{K}\\left(\\text{two significant figures}\\right)[\/latex]<\/p>\r\n[\/hidden-answer]\r\n<h4><strong>Check Your Learning<\/strong><\/h4>\r\nConvert 50 \u00b0F to \u00b0C and K.\r\n\r\n[reveal-answer q=\"143268\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"143268\"]10 \u00b0C, 280 K[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>ExAMPLe<\/h3>\r\nConvert [latex]50^\\circ F[\/latex] into degrees Celsius.\r\n[reveal-answer q=\"184814\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"184814\"]\r\n\r\nSolution\r\nWe will substitute [latex]50^\\circ F[\/latex] into the formula to find [latex]\\text{C}[\/latex].\r\n<table id=\"eip-id1168468775363\" class=\"unnumbered unstyled\" summary=\"The image shows the formula for converting degrees Fahrenheit to degrees Celsius which is c equals 5 ninths times the quantity f minus 32. Substitute 50 for f to get c equals 5 ninths times the quantity 50 minus 32. Simplify inside the parentheses to get c equals 5 ninths times 18. Multiply 5 ninths by 18 to get 10. The answer is c equals 10.\">\r\n<tbody>\r\n<tr>\r\n<td>Use the formula for converting \u00b0F to \u00b0C<\/td>\r\n<td>[latex]C=\\Large\\frac{5}{9}\\normalsize\\left(F - 32\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]\\color{red}{50}[\/latex] for \u00b0F.<\/td>\r\n<td>[latex]C=\\Large\\frac{5}{9}\\normalsize(\\color{red}{50}-32)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify in parentheses.<\/td>\r\n<td>[latex]C=\\Large\\frac{5}{9}\\normalsize\\left(18\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]C=10[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>A temperature of [latex]50\u00b0F[\/latex] is equivalent to [latex]10\u00b0C[\/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\u00a0IT<\/h3>\r\n[ohm_question]146880[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe weather forecast for Paris predicts a high of [latex]20^\\circ C[\/latex] Convert the temperature into degrees Fahrenheit.\r\n[reveal-answer q=\"741746\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"741746\"]\r\n\r\nSolution\r\nWe will substitute [latex]20^\\circ C[\/latex] into the formula to find [latex]F[\/latex].\r\n<table id=\"eip-id1168467239772\" class=\"unnumbered unstyled\" summary=\"The image shows the formula for converting degrees Celsius to degrees Fahrenheit which is f equals nine fifths times c plus 32. Substitute 20 for c to get f equals nine fifths times 20 plus 32. Multiply nine fifths by 20 first to get 36. Then add 36 plus 32 to get 68. The answer is f equals 68.\">\r\n<tbody>\r\n<tr>\r\n<td>Use the formula for converting \u00b0F to \u00b0C<\/td>\r\n<td>[latex]F=\\Large\\frac{9}{5}\\normalsize C+32[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]\\color{red}{20}[\/latex] for \u00b0C.<\/td>\r\n<td>[latex]F=\\Large\\frac{9}{5}\\normalsize(\\color{red}{20})+32[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]F=36+32[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]F=68[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>So [latex]20\u00b0C[\/latex] is equivalent to [latex]68\u00b0F[\/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]146881[\/ohm_question]\r\n\r\n<\/div>\r\n<h2>Contribute!<\/h2>\r\n<div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div>\r\n<a style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\" href=\"https:\/\/docs.google.com\/document\/d\/1UbG4Kv0Kn44RdYkt1497wKH4NxDsUpIa-WRm4ikefqQ\" target=\"_blank\" rel=\"noopener\">Improve this page<\/a><a style=\"margin-left: 16px;\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\" target=\"_blank\" rel=\"noopener\">Learn More<\/a>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Convert between the U.S. and the metric systems of measurement<\/li>\n<li>Convert between Fahrenheit and Celsius temperatures<\/li>\n<\/ul>\n<\/div>\n<p>Many measurements in the United States are made in metric units. A drink may come in [latex]\\text{2-liter}[\/latex] bottles, calcium may come in [latex]\\text{500-mg}[\/latex] capsules, and we may run a [latex]\\text{5-K}[\/latex] race. To work easily in both systems, we need to be able to convert between the two systems.<\/p>\n<p>The reference table below shows some of the most common conversions.<\/p>\n<table id=\"fs-id1412303\" summary=\"The table is labeled in the first row as\">\n<thead>\n<tr valign=\"top\">\n<th colspan=\"3\">Conversion Factors Between U.S. and Metric Systems<\/th>\n<\/tr>\n<tr valign=\"top\">\n<th>Length<\/th>\n<th>Weight<\/th>\n<th>Volume<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]1[\/latex] in = [latex]2.54[\/latex] cm<\/p>\n<p>[latex]1[\/latex] ft = [latex]0.305[\/latex] m<\/p>\n<p>[latex]1[\/latex] yd = [latex]0.914[\/latex] m<\/p>\n<p>[latex]1[\/latex] mi = [latex]1.61[\/latex] km<\/p>\n<p>[latex]1[\/latex] m = [latex]3.28[\/latex] ft<\/td>\n<td>[latex]1[\/latex] lb = [latex]0.45[\/latex] kg<\/p>\n<p>[latex]1[\/latex] oz = [latex]28[\/latex] g<\/p>\n<p>[latex]1[\/latex] kg = [latex]2.2[\/latex] lb<\/td>\n<td>[latex]1[\/latex] qt = [latex]0.95[\/latex] L<\/p>\n<p>[latex]1[\/latex] fl oz = [latex]30[\/latex] mL<\/p>\n<p>[latex]1[\/latex] L = [latex]1.06[\/latex] qt<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>We make conversions between the systems just as we do within the systems\u2014by multiplying by unit conversion factors.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Lee\u2019s water bottle holds [latex]500[\/latex] mL of water. How many fluid ounces are in the bottle? Round to the nearest tenth of an ounce.<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168466006710\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]500\\text{mL}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply by a unit conversion factor relating mL and ounces.<\/td>\n<td>[latex]500\\text{mL}\\cdot\\Large\\frac{1\\text{fl oz}}{30\\text{mL}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]\\Large\\frac{500\\text{fl oz}}{30}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td>[latex]16.7\\text{fl. oz.}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>The water bottle holds [latex]16.7[\/latex] fluid ounces.<\/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=\"ohm146876\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146876&theme=oea&iframe_resize_id=ohm146876&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146877\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146877&theme=oea&iframe_resize_id=ohm146877&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The conversion factors in the reference table\u00a0are not exact, but the approximations they give are close enough for everyday purposes. In the last example, we rounded the number of fluid ounces to the nearest tenth.<\/p>\n<div class=\"textbox exercises\">\n<h3>ExERCISE<\/h3>\n<p>Soleil lives in Minnesota but often travels in Canada for work. While driving on a Canadian highway, she passes a sign that says the next rest stop is in [latex]100[\/latex] kilometers. How many miles until the next rest stop? Round your answer to the nearest mile.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q462849\">Show Solution<\/span><\/p>\n<div id=\"q462849\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468500910\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\text{100 kilometers}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply by a unit conversion factor relating kilometers and miles.<\/td>\n<td>[latex]100\\text{kilometers}\\cdot    \\Large\\frac{1\\text{mile}}{1.61\\text{kilometers}}[\/latex]<\/p>\n<p>[latex]100\\cdot    \\Large\\frac{1\\text{mi}}{1.61\\text{km}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]\\Large\\frac{100\\text{mi}}{1.61}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td>[latex]62 \\text{mi}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>It is about [latex]62[\/latex] miles to the next rest stop.<\/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\u00a0IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146878\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146878&theme=oea&iframe_resize_id=ohm146878&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146879\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146879&theme=oea&iframe_resize_id=ohm146879&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h3>Convert Between Fahrenheit and Celsius Temperatures<\/h3>\n<p>Have you ever been in a foreign country and heard the weather forecast? If the forecast is for [latex]22^\\circ C[\/latex]. What does that mean?<\/p>\n<p>The U.S. and metric systems use different scales to measure temperature. The U.S. system uses degrees Fahrenheit, written [latex]^\\circ F[\/latex]. The metric system uses degrees Celsius, written [latex]^\\circ C[\/latex]. The image below\u00a0shows the relationship between the two systems.<\/p>\n<p>A temperature of [latex]37^\\circ C[\/latex] is equivalent to [latex]98.6^\\circ F[\/latex].<\/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\/24222516\/CNX_BMath_Figure_07_05_018.png\" alt=\"On the left side of the figure is a thermometer marked in degrees Celsius. The bottom of the thermometer begins with negative 20 degrees Celsius and ranges up to 100 degrees Celsius. There are tick marks on the thermometer every 5 degrees with every 10 degrees labeled. On the right side is a thermometer marked in degrees Fahrenheit. The bottom of the thermometer begins with negative 10 degrees Fahrenheit and ranges up to 212 degrees Fahrenheit. There are tick marks on the thermometer every 2 degrees with every 10 degrees labeled. Between the thermometers there is an arrow pointing on the left to 0 degrees Celsius and on the right to 32 degrees Fahrenheit. This is the temperature at which water freezes. Another arrow points on the left to 37 degrees Celsius and on the right to 98.6 degrees Fahrenheit. This is normal body temperature. A third arrow points on the left to 100 degrees Celsius and on the right to 212 degrees Fahrenheit. This is the temperature at which water boils.\" \/><br \/>\nIf we know the temperature in one system, we can use a formula to convert it to the other system.<\/p>\n<div class=\"textbox shaded\">\n<h3>Temperature Conversion<\/h3>\n<p>To convert from Fahrenheit temperature, [latex]\\text{F}[\/latex], to Celsius temperature, [latex]\\text{C}[\/latex], use the formula<\/p>\n<p>[latex]C=\\Large\\frac{5}{9}\\normalsize\\left(F - 32\\right)[\/latex]<br \/>\nTo convert from Celsius temperature, [latex]\\text{C}[\/latex], to Fahrenheit temperature, [latex]\\text{F}[\/latex], use the formula<\/p>\n<p>[latex]F=\\Large\\frac{9}{5}\\normalsize C+32[\/latex]<\/p>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Example:\u00a0<strong>Conversion from Celsius<\/strong><\/h3>\n<p>Normal body temperature has been commonly accepted as 37.0 \u00b0C (although it varies depending on time of day and method of measurement, as well as among individuals). What is this temperature on the kelvin scale and on the Fahrenheit scale?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q478867\">Show Answer<\/span><\/p>\n<div id=\"q478867\" class=\"hidden-answer\" style=\"display: none\">\n<p style=\"text-align: center;\">[latex]\\text{K}=\\text{ }^{\\circ}\\text{C}+273.15=37.0+273.2=\\text{310.2 K}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\text{ }^{\\circ}\\text{F}=\\frac{9}{5}^{\\circ}\\text{ C}+32.0=\\left(\\frac{9}{5}\\times 37.0\\right)+32.0=66.6+32.0=98.6^{\\circ}\\text{ F}[\/latex]<\/p>\n<\/div>\n<\/div>\n<h4>Check Your Learning<\/h4>\n<p>Convert 80.92 \u00b0C to K and \u00b0F.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q753412\">Show Answer<\/span><\/p>\n<div id=\"q753412\" class=\"hidden-answer\" style=\"display: none\">354.07 K, 177.7 \u00b0F<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Example:\u00a0<strong>Conversion from Fahrenheit<\/strong><\/h3>\n<p>Baking a ready-made pizza calls for an oven temperature of 450 \u00b0F. If you are in Europe, and your oven thermometer uses the Celsius scale, what is the setting? What is the kelvin temperature?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q43910\">Show Answer<\/span><\/p>\n<div id=\"q43910\" class=\"hidden-answer\" style=\"display: none\">\n<p style=\"text-align: center;\">[latex]\\text{ }^{\\circ}\\text{C}=\\frac{5}{9}(^{\\circ}\\text{ F}-\\text{32)}=\\frac{5}{9}\\left(450-32\\right)=\\frac{5}{9}\\times 418=232^{\\circ}\\text{ C}\\rightarrow\\text{set oven to 230}^{\\circ}\\text{ C}\\left(\\text{two significant figures}\\right)[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\text{K}=\\text{ }^{\\circ}\\text{ C}+273.15=230+273=\\text{503 K}\\rightarrow 5.0\\times {10}^{2}\\text{K}\\left(\\text{two significant figures}\\right)[\/latex]<\/p>\n<\/div>\n<\/div>\n<h4><strong>Check Your Learning<\/strong><\/h4>\n<p>Convert 50 \u00b0F to \u00b0C and K.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q143268\">Show Answer<\/span><\/p>\n<div id=\"q143268\" class=\"hidden-answer\" style=\"display: none\">10 \u00b0C, 280 K<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>ExAMPLe<\/h3>\n<p>Convert [latex]50^\\circ F[\/latex] into degrees Celsius.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q184814\">Show Solution<\/span><\/p>\n<div id=\"q184814\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nWe will substitute [latex]50^\\circ F[\/latex] into the formula to find [latex]\\text{C}[\/latex].<\/p>\n<table id=\"eip-id1168468775363\" class=\"unnumbered unstyled\" summary=\"The image shows the formula for converting degrees Fahrenheit to degrees Celsius which is c equals 5 ninths times the quantity f minus 32. Substitute 50 for f to get c equals 5 ninths times the quantity 50 minus 32. Simplify inside the parentheses to get c equals 5 ninths times 18. Multiply 5 ninths by 18 to get 10. The answer is c equals 10.\">\n<tbody>\n<tr>\n<td>Use the formula for converting \u00b0F to \u00b0C<\/td>\n<td>[latex]C=\\Large\\frac{5}{9}\\normalsize\\left(F - 32\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{50}[\/latex] for \u00b0F.<\/td>\n<td>[latex]C=\\Large\\frac{5}{9}\\normalsize(\\color{red}{50}-32)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify in parentheses.<\/td>\n<td>[latex]C=\\Large\\frac{5}{9}\\normalsize\\left(18\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]C=10[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>A temperature of [latex]50\u00b0F[\/latex] is equivalent to [latex]10\u00b0C[\/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\u00a0IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146880\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146880&theme=oea&iframe_resize_id=ohm146880&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>The weather forecast for Paris predicts a high of [latex]20^\\circ C[\/latex] Convert the temperature into degrees Fahrenheit.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q741746\">Show Solution<\/span><\/p>\n<div id=\"q741746\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nWe will substitute [latex]20^\\circ C[\/latex] into the formula to find [latex]F[\/latex].<\/p>\n<table id=\"eip-id1168467239772\" class=\"unnumbered unstyled\" summary=\"The image shows the formula for converting degrees Celsius to degrees Fahrenheit which is f equals nine fifths times c plus 32. Substitute 20 for c to get f equals nine fifths times 20 plus 32. Multiply nine fifths by 20 first to get 36. Then add 36 plus 32 to get 68. The answer is f equals 68.\">\n<tbody>\n<tr>\n<td>Use the formula for converting \u00b0F to \u00b0C<\/td>\n<td>[latex]F=\\Large\\frac{9}{5}\\normalsize C+32[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\\color{red}{20}[\/latex] for \u00b0C.<\/td>\n<td>[latex]F=\\Large\\frac{9}{5}\\normalsize(\\color{red}{20})+32[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]F=36+32[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]F=68[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>So [latex]20\u00b0C[\/latex] is equivalent to [latex]68\u00b0F[\/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=\"ohm146881\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146881&theme=oea&iframe_resize_id=ohm146881&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h2>Contribute!<\/h2>\n<div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div>\n<p><a style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\" href=\"https:\/\/docs.google.com\/document\/d\/1UbG4Kv0Kn44RdYkt1497wKH4NxDsUpIa-WRm4ikefqQ\" target=\"_blank\" rel=\"noopener\">Improve this page<\/a><a style=\"margin-left: 16px;\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\" target=\"_blank\" rel=\"noopener\">Learn More<\/a><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-15323\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 146881, 146880, 146879, 146878, 146877. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":167848,"menu_order":8,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"original\",\"description\":\"Question ID 146881, 146880, 146879, 146878, 146877\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"0eae8b6be31046febddfd31790aa69f9, 50c55893b9724655a18eeb17a746492e, 7463238538ea4b159747fd42213fbaaf","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-15323","chapter","type-chapter","status-publish","hentry"],"part":14880,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15323","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/users\/167848"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15323\/revisions"}],"predecessor-version":[{"id":15883,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15323\/revisions\/15883"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/parts\/14880"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapters\/15323\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/media?parent=15323"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/pressbooks\/v2\/chapter-type?post=15323"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/contributor?post=15323"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/wp-json\/wp\/v2\/license?post=15323"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}