Question

Prime factor of the denominator of rational number with decimal expansion 44.123 are
(a)2,3 (b)2,3,5 (c)2,5 (d)3,5
please help ☝️​

Answer 1

(c) 2, 5

The prime factors of the denominator of of the decimal expansion of 44.123 are 2 and 5.

Explanation:

• Here, the decimal number is 44.123 and when it is rationalised, we get the rational number 44123/1000.

• Here, 1000 = 2 × 2 × 2 × 5 × 5 × 5

• Thus in the prime factors of 1000, we get 2 thrice and 5 thrice.

• Therefore the prime factors are 2 and 5.

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

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

EVALUATION

Here the given number 44.123

The number can be rewritten as

$\sf \: 44.123 = \dfrac{44123}{1000}$

Now

Numerator = 44123

Denominator = 1000

We now prime factorise the denominator of the given number

$\sf \: 1000 = 2 \times 2 \times 2 \times 5 \times 5 \times 5$

$\sf \implies \: 1000 = {2}^{3} \times {5}^{3}$

Thus Prime factors of the denominator of a rational number with the decimal expansion  44.123 are 2 and 5

FINAL ANSWER

Hence the correct option is (c) 2,5

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