Decimal Numbers Quiz Set 016

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, $1/0.3$ is same as $0.3^{-1}$. The three powers of 0.3 given to us are -1, 1, 2 and 3. Out of these 3 is the most positive, so, $0.3^3$ 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: ${88 × 66 - 68 × 63}/13$ which equals ${1524/13}$, which is same as: $117{3/13}$

Comparing the given expression with $a^2 + 2 × a ×b + b^2 = (a + b)^2$, we see that if a = 9.74, and b = 0.3 then by inspection, x should be equal to 2b = 2 × 0.3 = 0.6.

The expression becomes $x = {8/1000} × {1/10}$ = 0.0008.