Question : The value of $\frac{(2.53)^3+(2.47)^3}{25.3 \times 25.3-624.91+24.7 \times 24.7}$ is 5 × 10k, where the value of k is:
Option 1: –2
Option 2: –1
Option 3: 1
Option 4: 2
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Correct Answer: –2
Solution : $\frac{(2.53)^3+(2.47)^3}{25.3 \times 25.3-624.91+24.7 \times 24.7}$ $\Rightarrow \frac{(2.53)^3+(2.47)^3}{25.3 \times 25.3-624.91+24.7 \times 24.7} = 5\times 10^{k}$ $\Rightarrow \frac{(2.53+2.47)(2.53^{2}+2.47^{2}-2.53\times 2.47)}{100\times2.53 \times 2.53-100\times6.2491+100\times2.47 \times 2.47} = 5\times 10^{k}$ $\Rightarrow \frac{(2.53+2.47)(2.53^{2}-6.2491+2.47^{2})}{10^{2}(2.53 \times 2.53-6.2491+2.47 \times 2.47)} = 5\times 10^{k}$ $\Rightarrow (2.53+2.47)\times10^{-2}=5\times 10^{k}$ $\Rightarrow 5\times10^{-2}=5\times 10^{k}$ $\therefore k=-2$ Hence, the correct answer is –2.
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