Question

What is the value of `1.875` in fractional form?

Answer 1

`1.875 = 15/8`

Explanation:

Given:

`1.875`

Since the last digit is `5`, this is half of a shorter decimal number, so multiply it by `2` to find:

`1.875 = 1/2 * 3.75`

`3.75` also ends with a `5`, so is half of a shorter decimal:

`3.75 = 1/2 * 7.5`

`7.5` also ends with `5`, so is half of a shorter decimal:

`7.5 = 1/2 * 15`

Having reached an integer, we can now deduce the simplest fraction:

`1.875 = 1/2 * 1/2 * 1/2 * 15 = 15/(2^3) = 15/8`

Answer 2

`1.875 = 15/8`

Explanation:

If you have a calculator, then here's an alternative method of finding the fraction for a decimal representation, using continued fractions...

Given:

`1.875`

Write down the whole number part `color(red)(1)`, subtract it and take the reciprocal to get approximately:

`1.14285714286`

Write down the whole number part `color(red)(1)`, subtract it and take the reciprocal to get approximately:

`6.99999999986`

We have obviously hit a rounding error and this value should be `7`, so write down `color(red)(7)` and stop.

We have found:

`1.875 = color(red)(1) + 1/(color(red)(1)+1/color(red)(7)) = 1+7/8 = 15/8`