Skill: Convert fractions to terminating decimals

To convert a fraction to a terminating decimal:

1. Reduce the fraction to lowest terms.
2. Look at the denominator. If its only prime factors are 2 and/or 5, the fraction can be written as a terminating decimal.
3. Multiply the numerator and denominator by the same number to make the denominator a power of 10, such as $(10)$, $(100)$, or $(1{,}000)$.
4. Write the numerator as a decimal using the denominator’s place value.

Example: Convert $\frac{3}{20}$ to a decimal

The fraction is already in lowest terms.

The denominator is $(20)$, and

$$20=2\cdot 2\cdot 5.$$

Its only prime factors are $2$ and $5$, so it will have a terminating decimal.

To change $(20)$ into $(100)$, multiply by $5$:

$$\frac{3}{20}\cdot\frac{5}{5}=\frac{15}{100}.$$

A denominator of $(100)$ means hundredths. Therefore,

$$\frac{15}{100}=0.15.$$

So,

$$\boxed{\frac{3}{20}=0.15}.$$

The value stays the same because the numerator and denominator were multiplied by the same number.