Q. 5.46 - Intermediate Algebra

Question

Convert to decimal form:

$ⓐ -9.5\times {10}^4 ⓑ 7.5\times {10}^{-2}$

Step-by-Step Solution

Answer

The decimal form of the given number $-9.5\times {10}^4=-95,000$

The decimal form of the given number $7.5\times {10}^{-2}=0.075$

Step 1. Given Information

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

$ⓐ -9.5\times {10}^4 ⓑ 7.5\times {10}^{-2}$

Part (a) Step 1. The given number is − 9 . 5 × 10 4

Determine the exponent, n, on the factor 10.

The exponent is $4$.

Since the exponent is positive, move the decimal point $4$ places to the right.

Add zeros as needed for placeholders.

$$\begin{gathered} -9.5\times {10}^4=-9.5\times 10000 \\ -9.5\times {10}^4=-95,000 \end{gathered}$$

Part (b) Step 1. The given number is 7 . 5 × 10 − 2

Determine the exponent, n, on the factor 10. 

The exponent is −2.

Since the exponent is negative, move the decimal point 2 places to the left.

Add zeros as needed for placeholders.

$$\begin{gathered} 7.5\times {10}^{-2}=7.5\times \frac{1}{{10}^2} \\ 7.5\times {10}^{-2}=7.5\times \frac{1}{100} \\ 7.5\times {10}^{-2}=0.075 \end{gathered}$$