What is $0.375$ as a fraction ?

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Answer 1 · 2017-10-24T19:44:59

$0.375 = 3/8$

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:

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

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