Decimal Numbers Quiz Set 018

y = 0.09 - (0.4 + 4.121) = -4.431.

Observe that all fractional numbers are having one digit to the right of the dot. So we can cancel all the dots and get a plain expression: ${94 × 98 - 73 × 89}/82$ which equals ${2715/82}$, which is same as: $33{9/82}$

Transposing, x = $1.49 × {0.0149/149}$ which gives 0.000149, which, in scientific form is $1.49 × 10^{-4}$.

We know ${a^3 - b^3}/{a^2 + ab + b^2}$ is same as ${(a - b) × (a^2 + ab + b^2)}/{a^2 + ab + b^2}$ which is same as a - b. So we get a - b = 7.91 - 0.50 = 7.41.

By inspection, the given ratio is same as ${0.70 × 0.70 × 0.70 + 0.03 × 0.03 × 0.03}/{5^3 × ({0.70 × 0.70 × 0.70 + 0.03 × 0.03 × 0.03})}$ which is $1/5^3$.