Question

One of these fractions is a repeating decimal; the other is terminating. Which is it? Without diving, how can you tell? `1/11`, `9/100`

Answer 1

`1/11`

Explanation:

I can immediately tell it'll be `1/11`. Whenever you divide something by `10`, the decimal places shifts 1 place to the left--aka the number is finite. When you divide by 100, the decimal shits 2 places to the left--therefore, it'll still be finite.

Therefore, `9/100 = 0.09`, which is finite. By elimination, `1/11` is the repeating decimal. In fact, if you calculate `1/11 = 0.090909...`, confirming what we derived above.

Hopefully this helps!

Answer 2

`9/100` is terminating. You can evenly divide anything by 100 just by moving the decimal place.

`1/11` is repeating.