Question

(b) 0.35555…
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.

Explanation:

1. For the first part (Can this be written as a fraction?): A repeating decimal (like \(0.35555\ldots\) where the digit 5 repeats) can be converted to a fraction. Terminating decimals can also be fractions, but non - repeating non - terminating decimals (irrational numbers) cannot. Since \(0.35555\ldots\) is a repeating decimal, the answer to "Can this be written as a fraction?" is Yes.
2. For the reason: The decimal \(0.35555\ldots\) has the digit 5 repeating after the first two decimal places. A terminating decimal has a finite number of decimal places (e.g., \(0.25\)), and a non - repeating non - terminating decimal has no pattern (like \(\pi\approx3.1415926\ldots\) without a repeating pattern). So the correct reason is that this is a repeating decimal.

Answer:

Can this be written as a fraction? : Yes
Give the reason: This is a repeating decimal.