How to Convert Fractions to their Decimal Form

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Converting Fractions to their Decimal Form

To do this, you simply divide the numerator (top number) by the denominator (bottom number).

Example 1: Terminating Decimal

To convert to a decimal, you calculate :

Example 2: Repeating Decimal

To convert to a decimal, you calculate :

(often written as )

Both terminating and repeating decimals are still rational numbers because their original form was a fraction.

Here are more examples of how to write a fraction as a decimal.

The key is to divide the numerator by the denominator.

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Examples with Terminating Decimals

A terminating decimal is a decimal that ends after a certain number of digits.

Example 1:

You divide 2 by 5.

Example 2:

You divide 7 by 8.

Example 3: (Improper Fraction)

You divide 15 by 4.

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Examples with Repeating Decimals

A repeating decimal is a decimal that has a digit or a group of digits that repeats forever. We use a bar over the repeating part to write it in a shorthand way.

Example 1:

You divide 1 by 3. The ‘3’ repeats forever.

Example 2:

You divide 5 by 6. The ‘3’ repeats.

Example 3:

You divide 3 by 11. The ’27’ pattern repeats.

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Example with a Mixed Number

To convert a mixed number, you can set the whole number aside and just convert the fraction part. Then, add the whole number back at the end.

Example:

1. Focus on the fraction:
2. Convert the fraction to a decimal:
3. Add the whole number back:

So, .