Chapter 1, Problem 8P

To determine

Add $(9.2{\text{×10}}^{\text{3}}\text{s)+(8}{\text{.3×10}}^{\text{4}}\text{s)+(0}{\text{.008×10}}^{\text{6}}\text{s)}$.

Answer to Problem 8P

$\text{1}{\text{.002×10}}^{\text{5}}\text{s}$

Explanation of Solution

Given:

$(9.2\times {10}^3\text{s})+(8.3\times {10}^4\text{s})+(0.008\times {10}^6\text{s})$

Calculation:

Let us first simplify the numbers separately and then add them.

$\begin{array}{c}9.2\times {10}^3\text{s }=9.2\times 1000\text{ s}\\ =9200\text{s}\end{array}$

Now, simplify $\text{8}{\text{.3×10}}^{\text{4}}\text{s}$.

$\begin{array}{c}\text{8}{\text{.3×10}}^{\text{4}}\text{s = 8}\text{.3}\times \text{10000 }\text{s}\\ \text{=83000 s}\end{array}$

Finally, simplify $\text{0}\text{.008 }\times {\text{ 10}}^{\text{6}}\text{s}$.

$\begin{array}{c}\text{0}\text{.008 }\times {\text{ 10}}^{\text{6}}\text{s}=0.008\times 1000000\text{s}\\ =8000\text{ s}\end{array}$

Now, add the simplified values to get the value of the given expression.

$\text{9200 s}+\text{83000 s}+\text{8000 s}=\text{100,200 s}$

The value of $\text{100,200 s}$ in scientific notation becomes $\text{1}{\text{.002×10}}^{\text{5}}\text{s}$.

Conclusion:

The value of the addition $\left(\text{9}\text{.2 }\times {\text{ 10}}^{\text{3}}\text{s}\right)\text{ + }\left(\text{8}\text{.3 }\times {\text{ 10}}^{\text{4}}\text{s}\right)\text{ + }\left(\text{0}\text{.008 }\times {\text{ 10}}^{\text{6}}\text{s}\right)$ is $\text{1}{\text{.002 × 10}}^{\text{5}}\text{s }$.