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CTET Paper II (Mathematics and Science) 15 Dec 2024 Shift 1 Solved Paper

Question : 48 of 150

Marks: +1, -0

The value of

\frac{0.125\times 57.8\times 0.729}{0.017\times 0.0081\times 0.25}

is equal to

Solution:

Concept:

Convert each decimal into an integer multiplied by a power of 10. Then simplify the fraction by cancelling common factors and powers of 10.

Explanation:

Rewrite each term:

0.125 = 125 \times 10^{-3}

57.8 = 578 \times 10^{-1}

0.729 = 729 \times 10^{-3}

0.017 = 17 \times 10^{-3}

0.0081 = 81 \times 10^{-4}

0.25 = 25 \times 10^{-2}

Numerator:

125 \times 578 \times 729 \times 10^{-3-1-3} = 125 \times 578 \times 729 \times 10^{-7}

Denominator:

17 \times 81 \times 25 \times 10^{-3-4-2} = 17 \times 81 \times 25 \times 10^{-9}

Expression becomes

\frac{125 \times 578 \times 729}{17 \times 81 \times 25} \times \frac{10^{-7}}{10^{-9}} = \frac{125}{25} \times \frac{578}{17} \times \frac{729}{81} \times 10^{2}

Simplify:

125/25 = 5

578/17 = 34

729/81 = 9

. Multiply:

5 \times 34 \times 9 = 1530

. Then

1530 \times 10^{2} = 153000

Answer:

The value is 153000, which is option B.

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