Question

How do you convert 29.2987 (987 being repeated) to a fraction?

Answer 1

`29.2bar(987) = 19513/666`

Explanation:

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

`(10000-10)*29.2bar(987)`

`=292987.bar(987) - 292.bar(987)`

`=292695`

The factor `10` is to shift the original number so that the repeating portion starts just after the decimal point. The factor `(1000-1)` is to further shift the number `3` places and subtract the original to cancel out the pattern that repeats every `3` digits.

Then dividing both ends by `(10000-10)` we find:

`29.2bar(987) = 292695/(10000-10) = 292695/9990 = (color(red)(cancel(color(black)(15)))*19513) / (color(red)(cancel(color(black)(15)))*666) = 19513/666`