Chapter 3.5, Problem 9QR

Solution

To Find: The value of (186,000)(31,000,000) in scientific form.

  $\left(186,000\right)\left(31,000,000\right)=5.766\times {10}^{12}$ in scientific form.

Given information:

(186,000)(31,000,000)

Concept and Formula Used:

Use the concept of decimals. In scientific notation, write the number as the power of 10. When the decimal is shifted to the right, subtract the power as many times as it is shift to the right and if the decimal is shifted to the left, add the power as many times as it is shifted to the left.

Calculation:

It is given that (186,000)(31,000,000).

  $\begin{array}{c}186,000=1.86\times {10}^5\\ 31,000,000=3.1\times {10}^7\\ \left(186,000\right)\left(31,000,000\right)=1.86\times {10}^5\times 3.1\times {10}^7=1.86\times 3.1\times {10}^{7+5}\\ \left(186,000\right)\left(31,000,000\right)=5.766\times {10}^{12}\end{array}$

Conclusion:

  $\left(186,000\right)\left(31,000,000\right)=5.766\times {10}^{12}$ in scientific form.