Decimal Numbers Quiz Set 003

The expression becomes $x = {41/41} × {10/100}$ = 0.1.

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: ${48 × 67 - 67 × 85}/73$ which equals ${-2479/73}$, which is same as: $-33{70/73}$

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, $1/0.077$ is same as $0.077^{-1}$. The three powers of 0.077 given to us are -1, 1, 2 and 3. Out of these 3 is the most positive, so, $0.077^3$ is the smallest.

We know $a^2 - b^2$ = $(a - b) × (a + b)$. So ${a^2 - b^2}/{a - b}$ is same as a + b. We get a + b = 2.44 + 1.86 = 4.30.

z = (0.2 + 9.477) - 0.02 = 9.657.