Question

(a) 0.373737…
can this be written as a fraction?
○yes ○no
give the reason.
○ this is a terminating decimal.
○ this is a repeating decimal.
○ this is a decimal that neither terminates nor repeats.
(b) 0.92847…
can this be written as a fraction?
○yes ○no
give the reason.
○ this is a terminating decimal.
○ this is a repeating decimal.

Explanation:

Part (a)

For the decimal \(0.373737\ldots\), it is a repeating decimal (the "37" repeats). Repeating decimals are rational numbers, and all rational numbers can be expressed as a fraction. So the answer to "Can this be written as a fraction?" is Yes, and the reason is that it is a repeating decimal.

The decimal \(0.92847\ldots\) (assuming it neither terminates nor repeats, as no repeating pattern is shown) is an irrational number if it does not repeat or terminate. Irrational numbers cannot be written as a fraction of two integers. So the answer to "Can this be written as a fraction?" is No. The reason would be that it is a decimal that neither terminates nor repeats (assuming the "..." indicates non - repeating, non - terminating behavior; if there was a repeating pattern, the answer would change, but from the given, we assume no repeating pattern is present).

Answer:

Can this be written as a fraction?
Yes

Give the reason.
This is a repeating decimal.

Part (b)