How to Convert Fractions to Repeating Decimals

Yes, simplifying a fraction before converting it to a decimal can make the conversion process easier. For example, converting 3/6 to 1/2 simplifies the division process.

You can use long division, with the denominator as the divisor and the numerator as the dividend. When the remainder starts repeating, the decimal will also repeat.

If the numerator is less than the denominator, you add a decimal point and a zero to continue the division process.

If the denominator is a multiple of 3, 6, or 9, there is a good chance that the fraction will convert to a repeating decimal.

The result of converting 1/3 to a decimal is 0.3 repeating.

The result of converting 2/3 to a decimal is 0.6 repeating.

The result of converting 1/6 to a decimal is 0.1 repeating followed by 6 repeating.

The result of converting 1/9 to a decimal is 0.1 repeating.

The result of converting 2/9 to a decimal is 0.2 repeating.

The result of converting 4/9 to a decimal is 0.4 repeating.

The result of converting 17/99 to a decimal is 0.17 repeating.

The result of converting 25/99 to a decimal is 0.25 repeating.

The result of converting 247/999 to a decimal is 0.247 repeating.

No, not all fractions convert to repeating decimals. For example, 3/3 is 1, and 3/6 is 0.5, which are not repeating decimals.

The result of converting 1/12 to a decimal is 0.083 repeating.

The result of converting 1/15 to a decimal is 0.06 repeating.

The result of converting 1/18 to a decimal is 0.05 repeating.

A repeating decimal is identified by a bar over the repeating digits in the decimal representation.

Yes, when the denominator is a multiple of 9, the decimal representation often repeats the numerator or a pattern derived from the numerator.

Yes, simplifying a fraction before converting it to a decimal can make the conversion process easier. For example, converting 3/6 to 1/2 simplifies the division process.

You can use long division, with the denominator as the divisor and the numerator as the dividend. When the remainder starts repeating, the decimal will also repeat.