Chapter 7.2, Problem 41PPE

To determine

To Simplify: The expression $\left(0.2\times {10}^5\right)\left(4\times {10}^{-12}\right)$ and write the answer in scientific notation.

Answer to Problem 41PPE

The required answer is $0.8\times {10}^{-7}$ .

Explanation of Solution

Given information:

The expression $\left(0.2\times {10}^5\right)\left(4\times {10}^{-12}\right)$

Calculation:

  $\begin{array}{l}\left(0.2\times {10}^5\right)\left(4\times {10}^{-12}\right)\\ =\left(0.2\cdot 4\right)\times \left({10}^5\cdot {10}^{-12}\right)\end{array}$

(Commutative and associative properties of multiplication)

  $=0.8\times {10}^{5+\left(-12\right)}$

(Multiply and add exponents with same base)

  $=0.8\times {10}^{-7}$

(Simplify)