Question

How can you convert a decimal to fraction?

Answer 1

See explanation...

Explanation:

If it is a terminating decimal, then multiply it by a power of `10` to make it into an integer, use that power of `10` as the denominator, then simplify it by dividing the numerator and denominator by any common factors.

For example:

`0.16 = 16/100 = (color(red)(cancel(color(black)(4)))*4)/(color(red)(cancel(color(black)(4)))*25) = 4/25`

If it is a repeating decimal, then multiply by a power of `10` to shift the repeating part to just after the decimal point and by a power of `10` corresponding to the length of the repeating section, minus `1`, to get an integer, then divide and simplify.

For example:

`0.2345345345... = 0.2bar(345)`

Multiply by `10(1000-1) = 10000-10` to get an integer:

`(10000-10)0.2bar(345) = 2345.bar(345) - 2.bar(345) = 2343`

So, dividing by `10000-10` we find:

`0.2bar(345) = 2343/(10000-10) = 2343/9990 = (color(red)(cancel(color(black)(3)))*781)/(color(red)(cancel(color(black)(3)))*3330) = 781/3330`