Chapter 9.6, Problem 56SR

To determine

Evaluate and express in scientific notation and standard form

Answer to Problem 56SR

  $\text{Scientific notation}8.93\times {10}^8$

  $\text{Standard form}893000000$

Explanation of Solution

Given:

  $\left(1.9\times {10}^2\right)\left(4.7\times {10}^6\right)$ .

Concept Used:

To write a number in scientific notation, we move the decimal point after the first nonzero number and raise the exponent of 10 by the number of digits we move the decimal point. If we move the decimal point to the left, then we raise the positive exponent and if we move to the right, then we raise the negative exponent.

Calculation:

In order to find the value of $\left(1.9\times {10}^2\right)\left(4.7\times {10}^6\right)$ in scientific notation, we will multiply the decimal point and add the exponent of 10 by 10. So, we get

  $\begin{array}{l}\left(1.9\times {10}^2\right)\left(4.7\times {10}^6\right)\\ =8.93\times {10}^2\times {10}^6\\ =8.93\times {10}^{2+6}\\ =8.93\times {10}^8\end{array}$

Thus, in scientific notation, the given number can be written as, $8.93\times {10}^8$

  $\text{Standard form}893000000$