Chapter 9.5, Problem 45HP

To determine

The sum, difference, product and quotient of two numbers

Answer to Problem 45HP

Addition: $804\times {10}^2$

Subtraction: $796\times {10}^2$

Multiplication: $32\times {10}^6$

Division: $2\times {10}^2$

Explanation of Solution

Let the numbers be

  $\begin{array}{l}a=8\times {10}^4\\ b=4\times {10}^2\end{array}$

Addition:

  $\begin{array}{l}=a+b\\ =8\times {10}^4+4\times {10}^2\\ =80000+400\\ =80400\\ =804\times {10}^2\end{array}$

Subtraction:

  $\begin{array}{l}=a-b\\ =8\times {10}^4-4\times {10}^2\\ =80000-400\\ =79600\\ =796\times {10}^2\end{array}$

Multiplication:

  $\begin{array}{l}=a\times b\\ =\left(8\times {10}^4\right)\left(4\times {10}^2\right)\\ =32\times {10}^{4+2}\\ =32\times {10}^6\end{array}$

Division:

  $\begin{array}{l}=a/b\\ =\left(8\times {10}^4\right)/\left(4\times {10}^2\right)\\ =2\times {10}^{4-2}\\ =2\times {10}^2\end{array}$