Question

Prime factors of the denominator of a rational number with the decimal expansion $44.123$ are

• A. $2,3$
• B. $2,3,5$
• C. $2,5$
• D. $3,5$

Answer 1

The correct option is C

$2,5$

Step 1. Determine the prime factors of the denominator of a rational number with the decimal expansion.

A prime number is a number that has only two factors, that is, $1$ and the number itself.

First, write the decimal number in the rational form.

$44.123=\frac{44123}{1000}$

Now, write the factor of the denominator of a rational number.

$\begin{array}{rcl}1000& =& 10\times 10\times 10\\ & =& 2\times 5\times 2\times 5\times 2\times 5\\ & =& 2^3\times 5^3\end{array}$

The prime factors of the denominator of a rational number with the decimal expansion are $2\mathrm{and}5$.

Hence, the correct option is $\left(C\right)$.