Question

Write in scientific notation:

$ⓐ48,300ⓑ0.0129$

Short 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-by-step solution

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.4.83×104

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 1.29×10-2Now checking the notation.

Check:

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