Question

(c) 0.888
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) $0.1\overline{7}$
can this be written as a fraction?
○yes ○no
give the reason.
○ this is a terminating decimal.

Explanation:

Part (c)

Step1: Determine decimal type

0.888 has a finite number of decimal places, so it's a terminating decimal.

Step2: Relate to fraction

All terminating decimals can be written as fractions (e.g., \(0.888=\frac{888}{1000}\)).

Step1: Determine decimal type

\(0.1\overline{7}\) has a repeating digit (7), so it's a repeating decimal.

Step2: Relate to fraction

All repeating decimals can be written as fractions (e.g., let \(x = 0.1\overline{7}\), then \(10x=1.\overline{7}\), \(100x = 17.\overline{7}\), subtract to solve for \(x\)).

Answer:

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

Part (d)