How do I change a decimal in to a fraction. 333

For non-repeating decimal

0.333 = 333/1000

for repeating decimal 0.333 ...

let x = 0.333 ... (1)

multiply x with 10^n where n=number of unduplicated repeating digit.

in this case only 1 digit which is 3 so we multiply with 10^1 or 10

so 10x = 3.333 ... (2)

now

(2) - (1). 10x - x = 3.333 ... - 0.333 ...

9x = 3

x = 3/9 = 1/3 this is the fraction of 0.333 ...

Well, with recurring numbers, like. 333333 ..., instead of the fraction being / 100, it's actually out of 99 surprisingly.

So in that case, it turns into 33/99

If it were 0.6667,

it would be

66/99