Q. 5.44 - Intermediate Algebra

Question

Write in scientific notation:

$ⓐ 48,300 ⓑ 0.0129$

Step-by-Step Solution

Answer

The scientific notation of the given number is $4.83\times {10}^4$

The scientific notation of the given number is $1.29\times {10}^{-2}$

Step 1. Given Information

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

$ⓐ 48,300 ⓑ 0.0129$

Part (a) Step 1. The given number is 48 , 300

The original number, $48,300$, is greater than $1$ so we will have a positive power of .

Move the decimal point to get$4.83$, a number between 1 and 10.

Count the number of decimal places the point was moved.

The decimal moved $4$ places.

Write as a product with a power of 10.

$4.83\times {10}^4$

Part (a) Step 2: The scientific notation of the given number is Now checking the notation. 4 . 83 × 10 4

Check: 

$$\begin{gathered} = 4.83\times {10}^4 \\ = 4.83\times 10000 \\ = 48,300 \end{gathered}$$

Part (b) Step 1. The given number is 0 . 0129

The original number, $0.0129$, is between 0 and 1 so we will have a negative power of 10.

Move the decimal point to get $1.29$, a number between 1 and 10.

Count the number of decimal places the point was moved.

The decimal moved $2$ places.

Write as a product with a power of 10.

$1.29\times {10}^{-2}$

Part (b) Step 2: The scientific notation of the given number is 1 . 29 × 10 - 2 Now checking the notation.

Check: 

$$\begin{gathered} =1.29\times {10}^{-2} \\ =1.29\times \frac{1}{{10}^2} \\ =1.29\times \frac{1}{100} \\ =0.0129 \end{gathered}$$