If there are 10 apples in the fridge and 7 on the table, what is the ratio of apples in the fridge to all the apples?
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notice above, all we did, was isolate the "recurring part" to the right of the decimal point, so the repeating 09, ended up on the right of it.
now, let's say, "x" is a variable whose value is the recurring part, therefore then
now, the idea behind the recurring part is that, we then, once we have it all to the right of the dot, we multiply it by some power of 10, so that it moves it "once" to the left of it, well, the recurring part is 09, is two digits, so let's multiply it by 100 then,
and you can check that in your calculator.