Question

(c) 0.555
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.
(d) (0.2overline{3})
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:

Step1: Analyze 0.555

0.555 is a terminating decimal (ends after 3 digits). Terminating decimals can be converted to fractions.
$$0.555 = \frac{555}{1000} = \frac{111}{200}$$

Step2: Select answer for (c)

Since it is a terminating decimal, it can be written as a fraction.

Step3: Analyze $0.2\overline{3}$

$0.2\overline{3}$ means 0.2333..., a repeating decimal (3 repeats infinitely). Repeating decimals can be converted to fractions.
Let $x = 0.2\overline{3} = 0.2333...$
$$10x = 2.333...$$
$$100x = 23.333...$$
$$100x - 10x = 23.333... - 2.333...$$
$$90x = 21$$
$$x = \frac{21}{90} = \frac{7}{30}$$

Step4: Select answer for (d)

Since it is a repeating decimal, it can be written as a fraction.

Answer:

For (c) 0.555:

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

For (d) $0.2\overline{3}$:

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