The value of \(\displaystyle\frac{(0.1\times0.1\times0.1+0.02\times0.02\times0.02)}{(0.2\times0.2\times0.2+0.04\times0.04\times0.04)}\) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.125
Every number in the denominator is twice the matching number in the numerator (0.2 = 2 × 0.1 and 0.04 = 2 × 0.02). Doubling a number makes its cube \(2^3=8\) times as large, so the whole denominator is 8 times the numerator, and no cube needs to be worked out.
Denominator written with the numerator’s numbers: \(8\times(0.1^3+0.02^3)\)
Value of the fraction: \(\displaystyle\frac{0.1^3+0.02^3}{8\times(0.1^3+0.02^3)}=\frac{1}{8}=0.125\)