Decimal Numbers Quiz Set 015

By simple addition we get $9.326 + 0.7 + 0.03 = 10.056$.

By simple addition we get $4.823 + 0.7 + 0.05 = 5.573$.

We know that if a number is less than 1, then it becomes smaller and smaller as it is raised to higher and higher positive powers. Now, $1/0.001$ is same as $0.001^{-1}$. The three powers of 0.001 given to us are -1, 1, 2 and 3. Out of these 3 is the most positive, so, $0.001^3$ is the smallest.

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: ${(-82) × 72 - 32 × (-34)}/25$. We can now simpilfy the minus signs to get ${(32 × 34) - (82 × 72)}/25$ which equals ${-4816/25}$, which is same as: $-192{16/25}$

By inspection, the given ratio is same as ${0.60 × 0.60 × 0.60 + 0.04 × 0.04 × 0.04}/{7^3 × ({0.60 × 0.60 × 0.60 + 0.04 × 0.04 × 0.04})}$ which is $1/7^3$.