Question : The value of $\frac{6.35 \times 6.35 \times 6.35+3.65 \times 3.65 \times 3.65}{63.5 \times 63.5+36.5 \times 36.5-63.5 \times 36.5}$ is equal to:
Option 1: 0.1
Option 2: 10
Option 3: 1
Option 4: 0.01
Correct Answer: 0.1
Solution : $\frac{6.35 \times 6.35 \times 6.35+3.65 \times 3.65 \times 3.65}{63.5 \times 63.5+36.5 \times 36.5-63.5 \times 36.5}$ = $\frac{(6.35 \times 6.35+3.65 \times 3.65-6.35 \times 3.65)(6.35+3.65)}{(6.35 \times 6.35+3.65 \times 3.65-6.35 \times 3.65)(10 \times 10)}$ = $\frac{6.35+3.65}{100}$ = $\frac{1}{10}$ = 0.1 Hence, the correct answer is 0.1.
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Question : The value of $\frac{5.35 \times 5.35 \times 5.35+3.65 \times 3.65 \times 3.65}{53.5 \times 53.5+36.5 \times 36.5-53.5 \times 36.5}$ is:
Option 1: 0.09
Option 2: 0.9
Option 3: 90
Option 4: 9
Question : $\frac{4.41 × 0.16}{2.1 ×1.6 × 0.21}$ is simplified to:
Option 1: 1
Option 2: 0.1
Option 3: 0.01
Option 4: 10
Question : (0.1 × 0.01 × 0.001 × 107) is equal to:
Option 1: 100
Option 2: 10–1
Option 3: 10–2
Question : What is the value of $\frac{(0.5)^{3}-(0.1)^{3}}{(0.5)^{2}+0.5\times 0.1+(0.1)^{2}}$?
Option 1: $0.1$
Option 2: $0.4$
Option 3: $0.5$
Option 4: $0.6$
Question : The value of $\frac{2}{3} \div \frac{3}{10}$ of $\frac{4}{9}-\frac{4}{5} \times 1 \frac{1}{9} \div \frac{8}{15}+\frac{3}{4} \div \frac{1}{2}$ is:
Option 1: $\frac{29}{6}$
Option 2: $\frac{17}{9}$
Option 3: $\frac{14}{3}$
Option 4: $\frac{49}{12}$
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