This page provides a simple overview of conversion between fractions and decimals.

A fraction is converted to the equivalent decimal by long division method.

A decimal is converted into its equivalent fraction by introducing the denominator based on the number of digits after decimal points.

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What are "decimal numbers"?

- multiples of primes
- standardized fractions
- standardized fractions

The answer is "decimal numbers are standardized fractions".

What is the decimal representation of `1/2`?

Note: By first principles, decimals are fractions with denominator `10`, `100`, `1000` etc. Since the denominator is standardized, it is dropped and is represented with a decimal point.

- `0.12`
- `0.5`
- `0.5`

The answer is "`0.5`".

By first principles, `1/2` is converted to the equivalent fraction `5/10`, which is `0.5` in decimals.

Convert the fraction `3/8` to decimal?

- `0.375`
- `0.375`
- `0.125`

The answer is "`0.375`".

This is explained in next page.

Considering converting the fraction `3/8` to decimal.

By first principles, the fraction has to be converted into an equivalent fraction having denominator one of `10`, `100`, `1000`, etc.

`8` is not a factor of `10`. So the fraction cannot be converted to an equivalent fraction with denominator `10`

`8` is not a factor of `100` either. So the fraction cannot be converted to an equivalent fraction with denominator `100`.

`8` is a factor of `1000 = 8xx125`. So, the denominator and numerator are multiplied by `125`.

`3/8 = (3xx125)/(8xx125) = 375/1000`

`375/1000 = 3/10 + 7/100 + 5/1000`

`=0.375` in decimal Noting the above, a simplified procedure is devised: By long division method, the decimal is calculated. This is shown in the figure.

**Converting a Fraction to a Decimal -- simplified procedure** : A fraction is converted to the equivalent decimal by long division method. An example, converting `3/8` to decimal is given in the figure.

Convert `5/4` into decimal.

- `0.125`
- `1.25`
- `1.25`

The answer is "`1.25`".

By long division method,

Convert `35/2` into decimal.

- `0.175`
- `17.5`
- `17.5`

The answer is "`17.5`".

By long division method,

We learned that the fractions can be converted to decimals. Similarly, decimals can be converted to fractions too.

Convert `6.75` in to the equivalent fraction

- `675/1000 = 27/40`
- `6 + 75/100 = 6 3/4`
- `6 + 75/100 = 6 3/4`

The answer is "`6 3/4`"

**Converting a Decimal to a Fraction** : The decimal is represented in its equivalent fraction form and the fraction is simplified.

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