Question

How do you convert 2.7812 (12 repeating) to a fraction?

Answer 1

The answer is `4589/1650`

Explanation:

Consider `x=2.781212...`
`10^2x=278.1212...`
`10^4x=27812.1212...`
the difference will give us :
`10^4x-10^2x=27812.1212...-278.1212...=27534`
so : `9900x=27534`
therefore : `x=27534/9900=4589/1650`