Skill: Convert fractions to decimals

A fraction means division:

$$\frac{\text{numerator}}{\text{denominator}}=\text{numerator}\div\text{denominator}.$$

To convert a fraction to a decimal, divide the numerator by the denominator. First simplify the fraction if possible. Then notice:

• If the simplified denominator has only factors of $2$ and/or $5$, the decimal terminates.
• Otherwise, the decimal repeats.

Example: Convert $\frac{5}{12}$ to a decimal

1. Interpret the fraction as division:

$$\frac{5}{12}=5\div12$$

2. Since $5$ is less than $12$, write $0.$ in the answer and add a decimal point to $5$:

$$5.000\div12$$

3. Divide step by step:

   • $12$ goes into $50$ four times. Write $4$ after the decimal.
     $4\times12=48$, leaving a remainder of $2$.
   • Bring down a $0$ to make $20$. $12$ goes into $20$ one time.
     $1\times12=12$, leaving a remainder of $8$.
   • Bring down a $0$ to make $80$. $12$ goes into $80$ six times.
     $6\times12=72$, leaving a remainder of $8$.
   • The remainder is $8$ again, so the $6$ will continue repeating.

Therefore,

$$\frac{5}{12}=0.41666\ldots=0.41\overline{6}.$$

The bar shows which digit repeats. You can check the answer because multiplying the decimal by $12$ gives $5$:

$$0.41666\ldots\times12=5.$$