Q. 5.45 - Intermediate Algebra

Question

Convert to decimal form:

$ⓐ 1.3 \times {10}^3 ⓑ -1.2 \times {10}^{-4}$

Step-by-Step Solution

Answer

The decimal form of the given number $1.3 \times {10}^3=1300$

The decimal form of the given number $-1.2 \times {10}^{-4}=-0.00012$

Step 1. Given Information

In the given question we have to convert the given number in decimal form:

$ⓐ 1.3 \times {10}^3 ⓑ -1.2 \times {10}^{-4}$

Part (a) Step 1. The given number is 1 . 3   ×   10 3

Determine the exponent, n, on the factor 10.

The exponent is 3.

Since the exponent is positive, move the decimal point 3 places to the right.

Add zeros as needed for placeholders.

$$\begin{gathered} 1.3 \times {10}^3=1.3\times 1000 \\ 1.3 \times {10}^3=1300 \end{gathered}$$

Part (b) Step 1. The given number is − 1 . 2   ×   10 − 4

Determine the exponent, n, on the factor 10. 

The exponent is $-4$.

Since the exponent is negative, move the decimal point $4$ places to the left.

Add zeros as needed for placeholders.

$$\begin{gathered} -1.2 \times {10}^{-4}=-1.2\times \frac{1}{{10}^4} \\ -1.2 \times {10}^{-4}=-1.2\times \frac{1}{10000} \\ -1.2 \times {10}^{-4}=-0.00012 \end{gathered}$$