Q. 5.43 - Intermediate Algebra

Question

Write in scientific notation:

$ⓐ 96,000 ⓑ 0.0078$

Step-by-Step Solution

Answer

The scientific notation of the given number $9.6\times {10}^4$

The scientific notation of the given number $7.8\times {10}^{-3}$

Step 1. Given Information

In the given question we have to write in scientific notation:

$ⓐ 96,000 ⓑ 0.0078$

Part (a) Step 1. The given number is 96 , 000

The original number, $96,000$, is greater than $1$ so we will have a positive power of $10$.

Move the decimal point to get $9.6$, a number between 1 and 10.

Count the number of decimal places the point was moved.

The number moved $4$ places.

Write as a product with a power of 10.

$9.6\times {10}^4$

Part (a) Step 2: The scientific notation of the given number is 9 . 6 × 10 4 . Now checking the notation.

Check:

$$\begin{gathered} =9.6\times {10}^4 \\ =9.6\times 10000 \\ =96000 \end{gathered}$$

Part (b) Step 1. The given number is 0 . 0078

The original number, $0.0078$, is between 0 and 1 so we will have a negative power of 10.

Move the decimal point to get $7.8$, a number between 1 and 10.

Count the number of decimal places the point was moved.

The decimal moved $3$ places.

Write as a product with a power of 10.

$7.8\times {10}^{-3}$

Part (b) Step 2: The scientific notation of the given number is 7 . 8 × 10 - 3 Now checking the notation.

Check:

$$\begin{gathered} =7.8\times {10}^{-3} \\ =7.8\times \frac{1}{{10}^3} \\ =7.8\times \frac{1}{1000} \\ =7.8\times 0.001 \\ =0.0078 \end{gathered}$$