Converting Between Fractions and Decimals

Fractions and decimals are two different ways to represent the exact same rational number. Knowing how to quickly convert between them is an essential math skill.

Converting Fractions to Decimals

To convert a fraction to a decimal, treat the fraction bar as a division symbol. Simply divide the numerator (the top number) by the denominator (the bottom number).

When you divide, you will encounter two types of decimals:

1. Terminating Decimals: The division eventually leaves a remainder of zero, meaning the decimal ends.
2. Repeating Decimals: The division never ends, and a digit or a block of digits repeats infinitely.

Example 1: Convert $\frac{3}{8}$ to a decimal. Divide $3$ by $8$: $3 \div 8 = 0.375$ Because the division ends with no remainder, $0.375$ is a terminating decimal.

Example 2: Convert $\frac{5}{6}$ to a decimal. Divide $5$ by $6$: $5 \div 6 = 0.8333\ldots$ The digit $3$ repeats forever. We write this repeating decimal using a bar over the repeating part: $0.8\overline{3}$.

Converting Decimals to Fractions

To convert a terminating decimal to a fraction, use the place value of the final digit to determine your denominator, and then simplify the fraction.

Example 3: Convert $0.625$ to a fraction in simplest form.

1. Identify the place value of the last digit. In $0.625$, the $5$ is in the "thousandths" place.
2. Write the decimal digits as the numerator, and the place value as the denominator: $\frac{625}{1000}$
3. Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (which is $125$): $\frac{625 \div 125}{1000 \div 125} = \frac{5}{8}$

So, $0.625$ is equal to $\frac{5}{8}$.