Question

If the repeating decimal 0.23737 is written as a fraction in lowest terms, what is the sum of the numerator and the denominator?

Answer 1

Let
`x=0.23737\ldots=0.2\overline{37}`. Then

`10x=2.\overline{37}`

`100x=237.\overline{37}`

`\implies100x-10x=237.\overline{37}-2.\overline{37}`

`\implies90x=235`

`\implies x=(235)/(90)=(47)/(18)`

and the sum of the numerator and denominator is 65.

Answer 2

the answer is 23/99

Explanation: