Question

What is the value of
$\frac{(0.1\times0.1\times0.1+0.03\times0.03\times0.03)}{(0.3\times0.3\times0.3+0.09\times0.09\times0.09)}$

• A. 0.027
• B. 0.009
• C. 0.729
• D. 0.037

Answer 1

Answer:

D. 0.037

We need to evaluate

$\frac{(0.1^3+0.03^3)}{(0.3^3+0.09^3)}.$

Notice that

$0.3 = 3(0.1), \qquad 0.09 = 3(0.03).$

Therefore,

$0.3^3 = 3^3(0.1^3)=27(0.1^3),$

and

$0.09^3 = 3^3(0.03^3)=27(0.03^3).$

So the denominator becomes

$0.3^3+0.09^3$
$=27(0.1^3)+27(0.03^3)$
$=27(0.1^3+0.03^3).$

Hence,

$\frac{0.1^3+0.03^3}{0.3^3+0.09^3}$

$\frac{0.1^3+0.03^3}{27(0.1^3+0.03^3)}$

$\frac{1}{27}=0.037$