Question

(a) 0.646464…
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) 0.43721…
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.
(c) 0.555

Explanation:

Step1: Analyze 0.646464...

The decimal 0.646464... has a repeating pattern "64", so it is a repeating decimal. All repeating decimals can be expressed as fractions.

Step2: Analyze 0.43721...

The decimal 0.43721... has no indicated repeating pattern and does not terminate, so it is a non-terminating, non-repeating decimal. Such decimals are irrational and cannot be written as fractions.

Answer:

(a) Can this be written as a fraction? Yes
Give the reason. This is a repeating decimal.
(b) Can this be written as a fraction? No
Give the reason. This is a decimal that neither terminates nor repeats.