Chapter 7.2, Problem 40PPE

To determine

To Simplify: The expression $\left(0.5\times {10}^{-6}\right)\left(0.3\times {10}^{-2}\right)$ and write the answer in scientific notation.

Answer to Problem 40PPE

The required answer is $1.5\times {10}^{-9}$ .

Explanation of Solution

Given information:

The expression $\left(0.5\times {10}^{-6}\right)\left(0.3\times {10}^{-2}\right)$

Calculation:

  $\begin{array}{l}\left(0.5\times {10}^{-6}\right)\left(0.3\times {10}^{-2}\right)\\ =\left(0.5\cdot 0.3\right)\times \left({10}^{-6}\cdot {10}^{-2}\right)\end{array}$

(Commutative and associative properties of multiplication)

  $=0.15\times {10}^{-6+\left(-2\right)}$

(Multiply and add exponents with same base)

  $=0.15\times {10}^{-8}$

(Simplify)

  $=1.5\times {10}^{-9}$

(Write in scientific notation)