Question

Consider the following statements:
1. $\frac{1}{33}$ cannot be written as a Terminating decimal.
2. $\frac{2}{15}$ can be written as a Terminating decimal.
3. $\frac{1}{16}$ can be written as a Terminating decimal.
Which of the statements given above is/are correct?

• A. 1 only
• B. 2 only
• C. 1 and 3 only
• D. 2 and 3 only

Answer 1

The correct option is C 1 and 3 only

For a rational number to have a terminating decimal expansion, the denominator has to be of the form $2^m\times 5^n$
Where m and n are whole numbers
Here, in
$\frac{1}{33}$
Denominator, $33=3\times 11$
So, non-terminating decimal expansion
$\frac{2}{15}$
Denominator, $15=3\times 5$
So, non-terminating decimal expansion
$\frac{1}{16}$
Denominator, $16=2^4$
Hence, it will have a terminating decimal expansion.
Hence, correct option is C