Mentally approximate the quotient without a calculator. $\left( 14 \times 10 ^ { - 10 } \right) \div \left( 0.7 \times 10 ^ { - 30 } \right)$
A) $13.3 \times 10 ^ { 40 }$
B) $2 \times 10 ^ { 9 }$
C) $2 \times 10 ^ { 20 }$
D) $2 \times 10 ^ { 21 }$
E) $13.3 \times 10 ^ { 20 }$

Question

Quizplus · Accepted Answer

First, simplify the expression using the rules of exponents:

\begin{align*}
\left( 14 	imes 10 ^ { - 10 } ight) \div \left( 0.7 	imes 10 ^ { - 30 } ight) &= \frac{14}{0.7} 	imes 10 ^ {-10+30}\
&=20 	imes 10 ^ {20} \
&= 2 	imes 10 ^ {21}
\end{align*}

The closest answer choice to this approximation is D, so the best choice is D.

Mentally Approximate the Quotient Without a Calculator (14×10−10)÷(0.7×10−30)\left( 14 \times 10 ^ { - 10 } \right) \div \left( 0.7 \times 10 ^ { - 30 } \right)(14×10−10)÷(0.7×10−30)

Mentally Approximate the Quotient Without a Calculator $\left( 14 \times 10 ^ { - 10 } \right) \div \left( 0.7 \times 10 ^ { - 30 } \right)$