Skill: Convert simple decimals into fractions

A terminating decimal can be written as a fraction by using its place value.

• One digit after the decimal point means tenths, so use a denominator of $10$.
• Two digits means hundredths, so use a denominator of $100$.
• Three digits means thousandths, so use a denominator of $1{,}000$.

Example: Convert $0.75$ to a fraction.

1. There are two digits after the decimal point, so the denominator is $100$:

$$0.75=\frac{75}{100}$$

2. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, $25$:

$$\frac{75\div25}{100\div25}=\frac{3}{4}$$

Therefore,

$$0.75=\frac{3}{4}$$

The decimal digits become the numerator, and the number of decimal places tells you the denominator.