Question

What is `0.375` as a fraction ?

Answer 1

`0.375 = 3/8`

Explanation:

Here's a general method for converting terminating decimal expansions into fractions...

• If the last non-zero decimal digit is `2,4,6` or `8`, then write down `color(red)(5)` and multiply by it.

• If the last non-zero decimal digit is `5`, then write down `color(red)(2)` and multiply by it.

• If the last non-zero digit is something else (i.e. `1`, `3`, `7` or `9`) then write down `color(red)(10)` and multiply by it.

• Repeat until you end up with an integer.

• Multiply all the `color(red)(5)`'s, `color(red)(2)`'s or `color(red)(10)`'s you found together to form the denominator of your fraction and use the integer you ended up with as the numerator.

So in our example:

• `0.375` ends with `5`, so write down `color(red)(2)` and double `0.375` to get `0.75`

• `0.75` ends with `5`, so write down `color(red)(2)` and double `0.75` to get `1.5`

• `1.5` ends with `5`, so write down `color(red)(2)` and double `1.5` to get `3`.

• Having reached an integer `3`, we find the required fraction is:

  `3/(color(red)(2) * color(red)(2) * color(red)(2)) = 3/8`