Lesson 43: Converting Decimals to Fractions, Converting Fractions to Decimals, Converting Percents to Decimals

New Concept

Fractions, decimals, and percents are different ways to write the same value. We can convert between them to suit various mathematical problems.

• Decimal to Fraction: To write a decimal number as a fraction, write the digits after the decimal point as the numerator. For the denominator, write the place value of the last digit.
• Fraction to Decimal: To change a fraction to a decimal number, perform the division indicated by the fraction.
• Percent to Decimal: A percent may be written as a decimal by using the same digits but shifting the decimal point two places to the left. For example, $45\% = \frac{45}{100} = 0.45$.

What’s next

This is just the start. Next, we'll apply these skills in worked examples with mixed numbers, probabilities, and repeating decimals.

Property

To write a decimal number as a fraction, we write the digits after the decimal point as the numerator of the fraction. For the denominator of the fraction, we write the place value of the last digit. Then we reduce.

Examples

$0.6 = \frac{6}{10} = \frac{3}{5}$
$0.375 = \frac{375}{1000} = \frac{3}{8}$
$7.25 = 7\frac{25}{100} = 7\frac{1}{4}$

Explanation

Think of a decimal as having a secret fraction identity! The numbers after the dot are the top part (numerator). The bottom part (denominator) comes from the place value of the very last digit. If it’s in the tenths place, use 10. Hundredths place? Use 100! Then, just simplify the fraction to its tidiest form.

Property

To change a fraction to a decimal number, we perform the division indicated by the fraction. The fraction $\frac{1}{4}$ indicates that 1 is divided by 4. Every fraction of whole numbers converts to either a terminating decimal or a repeating decimal.

Examples

$\frac{3}{5} \rightarrow 3 \div 5 = 0.6$
$\frac{5}{9} \rightarrow 5 \div 9 = 0.555... = 0.\bar{5}$
$2\frac{1}{4} = \frac{9}{4} \rightarrow 9 \div 4 = 2.25$

Explanation

A fraction is just a division problem waiting to happen! To uncover its decimal form, simply divide the top number (numerator) by the bottom number (denominator). You might get a nice, clean answer that stops, called a terminating decimal. Or, you could get a number that repeats forever in a pattern, which we mark with a cool bar on top.