Converting Between Fractions and Decimals

Fractions and decimals are two different ways to show the exact same value. Knowing how to convert between them makes comparing numbers and solving math problems much easier.

Converting Fractions to Decimals

To change a fraction into a decimal, simply think of the fraction bar as a division sign. You divide the numerator (the top number) by the denominator (the bottom number).

Example: Convert $\frac{3}{8}$ to a decimal.

Set up the division problem $3 \div 8$. Since $8$ does not go into $3$, you add a decimal point and zeros to the $3$:

$3.000 \div 8 = 0.375$

So, $\frac{3}{8} = 0.375$.

Converting Decimals to Fractions

To change a decimal into a fraction, look at the place value of the last digit. Write the decimal digits over the appropriate power of ten ($10$, $100$, $1000$, etc.), and then simplify the fraction.

Example: Convert $0.625$ to a fraction in simplest form.

The last digit ($5$) is in the thousandths place, so write $625$ over $1000$:

$0.625 = \frac{625}{1000}$

Now, simplify the fraction by dividing the numerator and denominator by their greatest common factor. Both numbers can be divided by $125$:

$\frac{625 \div 125}{1000 \div 125} = \frac{5}{8}$

Comparing Fractions and Decimals

When you need to compare a fraction and a decimal, the easiest method is to convert the fraction into a decimal so both numbers are in the same format.

Example: Which is greater, $\frac{5}{8}$ or $0.6$?

First, convert $\frac{5}{8}$ to a decimal by dividing $5$ by $8$:

$5 \div 8 = 0.625$

Now compare the two decimals: $0.625$ and $0.600$.

Since $0.625$ is greater than $0.600$, we know that $\frac{5}{8}$ is greater than $0.6$.