We often need to rewrite decimals as fractions or mixed numbers. Let’s go back to our lunch order to see how we can convert decimal numbers to fractions. We know that [latex]$5.03[/latex] means [latex]5[/latex] dollars and [latex]3[/latex] cents. Since there are [latex]100[/latex] cents in one dollar, [latex]3[/latex] cents means [latex]{\Large\frac{3}{100}}[/latex] of a dollar, so [latex]0.03={\Large\frac{3}{100}}[/latex].

We convert decimals to fractions by identifying the place value of the farthest right digit. In the decimal [latex]0.03[/latex], the [latex]3[/latex] is in the hundredths place, so [latex]100[/latex] is the denominator of the fraction equivalent to [latex]0.03[/latex].

[latex]0.03={\Large\frac{3}{100}}[/latex]

For our [latex]$5.03[/latex] lunch, we can write the decimal [latex]5.03[/latex] as a mixed number.

[latex]5.03=5{\Large\frac{3}{100}}[/latex]

Notice that when the number to the left of the decimal is zero, we get a proper fraction. When the number to the left of the decimal is not zero, we get a mixed number.

example

Write each of the following decimal numbers as a fraction or a mixed number:

1. [latex]4.09[/latex]
2. [latex]3.7[/latex]
3. [latex]-0.286[/latex]

Solution:

1.
[latex]4.09[/latex]
There is a [latex]4[/latex] to the left of the decimal point. Write “[latex]4[/latex]” as the whole number part of the mixed number.
Determine the place value of the final digit.
Write the fraction. Write [latex]9[/latex] in the numerator as it is the number to the right of the decimal point.
Write [latex]100[/latex] in the denominator as the place value of the final digit, [latex]9[/latex], is hundredth.	[latex]4{\Large\frac{9}{100}}[/latex]
The fraction is in simplest form.	So, [latex]4.09=4{\Large\frac{9}{100}}[/latex]

Did you notice that the number of zeros in the denominator is the same as the number of decimal places?

2.
[latex]3.7[/latex]
There is a [latex]3[/latex] to the left of the decimal point. Write “[latex]3[/latex]” as the whole number part of the mixed number.
Determine the place value of the final digit.
Write the fraction. Write [latex]7[/latex] in the numerator as it is the number to the right of the decimal point.
Write [latex]10[/latex] in the denominator as the place value of the final digit, [latex]7[/latex], is tenths.	[latex]3{\Large\frac{7}{10}}[/latex]
The fraction is in simplest form.	So, [latex]3.7=3{\Large\frac{7}{10}}[/latex]

3.
[latex]−0.286[/latex]
There is a [latex]0[/latex] to the left of the decimal point. Write a negative sign before the fraction.
Determine the place value of the final digit and write it in the denominator.
Write the fraction. Write [latex]286[/latex] in the numerator as it is the number to the right of the decimal point. Write [latex]1,000[/latex] in the denominator as the place value of the final digit, [latex]6[/latex], is thousandths.	[latex]-{\Large\frac{286}{1000}}[/latex]
We remove a common factor of [latex]2[/latex] to simplify the fraction.	[latex]-{\Large\frac{143}{500}}[/latex]

In the next video example, we who how to convert a decimal into a fraction.