Q20. - Algebra 1

Question

Evaluate each product or quotient. Express the results in scientific notation.

$\left(7.5\times {10}^6\right)\left(2.5\times {10}^{-2}\right)$

Step-by-Step Solution

Answer

The value of the given product $\left(7.5\times {10}^6\right)\left(2.5\times {10}^{-2}\right)$ in scientific notation is $1.875\times {10}^5$.

Step 1. Evaluate the given product 7.5 × 10 6 2.5 × 10 − 2 .

The value of the given product $\left(7.5\times {10}^6\right)\left(2.5\times {10}^{-2}\right)$ is:

$$\begin{gathered} \left(7.5\times {10}^6\right)\left(2.5\times {10}^{-2}\right)=7.5\times {10}^6\times 2.5\times {10}^{-2} \\ =7.5\times 2.5\times {10}^6\times {10}^{-2} \\ =18.75\times {10}^{6+\left(-2\right)}\left(\because a^m\times a^n=a^{m+n}\right) \\ =18.75\times {10}^{6-2} \\ =18.75\times {10}^4 \end{gathered}$$

Step 2. Express the result of the product 7.5 × 10 6 2.5 × 10 − 2 in scientific notation.

The result of the product $\left(7.5\times {10}^6\right)\left(2.5\times {10}^{-2}\right)$ is $18.75\times {10}^4$.

 

The result of the product $\left(7.5\times {10}^6\right)\left(2.5\times {10}^{-2}\right)$ in scientific notation is:

$$\begin{gathered} 18.75\times {10}^4=1.875\times 10\times {10}^4 \\ =1.875\times {10}^{1+4}\left(\because a^m\times a^n=a^{m+n}\right) \\ =1.875\times {10}^5 \end{gathered}$$

Therefore, the value of the given product $\left(7.5\times {10}^6\right)\left(2.5\times {10}^{-2}\right)$ in scientific notation is $1.875\times {10}^5$.