Convert fractions to decimals

Converting a fraction to a decimal means interpreting the numerator divided by the denominator and finding an equivalent base-ten representation by using equivalent fractions or division. The reasoning includes determining whether a simplified fraction produces a terminating or repeating decimal, recording repeating digits accurately, and checking equivalence by converting back or comparing values; irrational numbers and more advanced symbolic forms are outside this scope.

Detailed Explanation: 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

Interpret the fraction as division:

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

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

5.000\div12

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.

Learn by doing: Convert fractions to decimals

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Fraction to Decimals - Standard

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