Question

Question #141ba

Answer 1

`0.969696... = 96/99 = 32/33`

Explanation:

Here's what you do:

Since there are two decimals that repeat, write

`100 xx 0.969696... = 96.969696...`

and

`1 xx 0.969696... = 0.969696...`

Subtract these two statements:

99x0.969696... = 96#

as the remaining decimals have disappeared in the right-hand expression.

Divide each side by 99:

`0.969696... = 96 / 99`

which simplifies to `32/33`

Had there been three repeating decimals, you would start by multiplying by 1000 and so on.