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 $$5.03$ means $5$ dollars and $3$ cents. Since there are $100$ cents in one dollar, $3$ cents means ${\Large\frac{3}{100}}$ of a dollar, so $0.03={\Large\frac{3}{100}}$.

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

$0.03={\Large\frac{3}{100}}$

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

$5.03=5{\Large\frac{3}{100}}$

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. $4.09$
2. $3.7$
3. $-0.286$

Solution:

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

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

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

3.
$−0.286$
There is a $0$ 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 $286$ in the numerator as it is the number to the right of the decimal point. Write $1,000$ in the denominator as the place value of the final digit, $6$, is thousandths.	$-{\Large\frac{286}{1000}}$
We remove a common factor of $2$ to simplify the fraction.	$-{\Large\frac{143}{500}}$

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