Sure, let's break down the steps for simplifying the given expression using scientific notation:
[tex]\[ \frac{(1.3 \times 10^{-7})(2.4 \times 10^8)}{1.3 \times 10^9} \][/tex]
### Step-by-Step Solution:
1. Multiply the numerators:
[tex]\[
(1.3 \times 10^{-7})(2.4 \times 10^8)
\][/tex]
First, multiply the coefficients (the numbers in front):
[tex]\[
1.3 \times 2.4 = 3.12
\][/tex]
Next, multiply the powers of 10:
[tex]\[
10^{-7} \times 10^8 = 10^{-7+8} = 10^1 = 10
\][/tex]
Combining these results:
[tex]\[
(1.3 \times 10^{-7})(2.4 \times 10^8) = 3.12 \times 10^1 = 31.2
\][/tex]
2. Now divide by the denominator:
[tex]\[
\frac{31.2}{1.3 \times 10^9}
\][/tex]
First, divide the coefficients:
[tex]\[
\frac{31.2}{1.3} = 24
\][/tex]
Divide by the power of 10:
[tex]\[
\frac{24}{10^9} = 24 \times 10^{-9}
\][/tex]
3. Final expression in scientific notation:
Adjust the coefficient to be between 1 and 10:
[tex]\[
24 = 2.4 \times 10^1
\][/tex]
Therefore:
[tex]\[
2.4 \times 10^1 \times 10^{-9} = 2.4 \times 10^{-8}
\][/tex]
### Conclusion:
The simplified form of [tex]\(\frac{(1.3 \times 10^{-7})(2.4 \times 10^8)}{1.3 \times 10^9}\)[/tex] in scientific notation is:
[tex]\[ 2.4 \times 10^{-8} \][/tex]
