# Convert Fractions to Decimals

When we want to represent a part of a number, we usually use a fraction or a decimal. Some numbers are easier to talk about in terms of decimals (.07 is seven cents!) and others are easier to talk about in terms of fractions (if I eat 5 out of a dozen bagels, I ate $\dfrac{5}{12}$ of the bagels). Others numbers are as easily written as decimals or fractions: one half is $\dfrac{1}{2}$ or .5.

No matter how we represent numbers, you can always convert decimals to fractions and fractions to decimals. You can also easily convert decimals to percents once you have a number in decimal form.

When converting fractions to decimals, it's important to remember one rule: **every fraction is a division problem**.

$\dfrac{1}{2}=1\div 2$

$\dfrac{5}{6}=5\div 6$

$\dfrac{5}{12}=5\div 12$

$\dfrac{111}{242}=111\div 242$

$\dfrac{1,909,876}{2,562,323}=1,909,876\div 2,562,323$

And, once you complete the division problems, you will have the decimal equivalent of the fractions.

$\dfrac{1}{2}=1\div 2=.5$

$\dfrac{5}{6}=5\div 6=.8\overline{33}$

$\dfrac{5}{12}=5\div 12=.416667$

$\dfrac{111}{242}=111\div 242=.458678$

$\dfrac{1,909,876}{2,562,323}=1,909,876\div 2,562,323=.745369$

To check your work, remember, if the numerator (the number on top) is lower than the denominator (the number on the bottom) your decimal should be less than 1 whole.

If the numerator is larger than the denominator (an improper fraction) your answer should include an whole number. For instance:

$\dfrac{8}{7}=8\div 7=1.14286$

Overall, converting a fraction to a decimal is as simple as dividing the numerator by the denominator.

One note: when you do long division using the "house," you flip the numbers.

So:

$\dfrac{1}{2}=1\div 2= 2\vert\overline{\text{ }{1}\text{}}$

#### Practice Problems:

## Convert Fractions to Decimals

Change each fraction into a decimal. Round to the nearest thousandth.

1. $\dfrac{1}{2}=$

2. $\dfrac{1}{12}=$

3. $\dfrac{3}{4}=$

4. $\dfrac{2}{3}=$

5. $\dfrac{9}{16}=$

6. $\dfrac{1}{9}=$

7. $\dfrac{12}{17}=$

8. $\dfrac{4}{7}=$

9. $\dfrac{6}{10}=$

10. $\dfrac{3}{9}=$

11. $\dfrac{11}{12}=$

12. $\dfrac{2}{5}=$

#### Answer Key: