Question

What is the value of the expression simplified in Standard Notation: (3.2 × 10^−2)(4.2 × 10^6)/(5.2 × 10^5)
(1 point)

Answer 1

To simplify the expression \((3.2 \times 10^{-2})(4.2 \times 10^{6})/(5.2 \times 10^{5})\), we can follow these steps:

1. **Multiply the numerators**:
\[
(3.2 \times 10^{-2}) \times (4.2 \times 10^{6}) = (3.2 \times 4.2) \times (10^{-2} \times 10^{6})
\]
Calculating \(3.2 \times 4.2\):
\[
3.2 \times 4.2 = 13.44
\]
Now for the powers of 10:
\[
10^{-2} \times 10^{6} = 10^{-2 + 6} = 10^{4}
\]
So, the product becomes:
\[
13.44 \times 10^{4}
\]

2. **Now, divide by the denominator**:
\[
\frac{13.44 \times 10^{4}}{5.2 \times 10^{5}} = \frac{13.44}{5.2} \times \frac{10^{4}}{10^{5}}
\]
Calculating \(\frac{13.44}{5.2}\):
\[
13.44 \div 5.2 \approx 2.585
\]
Now for the powers of 10:
\[
\frac{10^{4}}{10^{5}} = 10^{4-5} = 10^{-1}
\]

3. **Combine the results**:
\[
2.585 \times 10^{-1}
\]
This can be written as:
\[
0.2585
\]

Thus, the value of the expression in standard notation is:
\[
\boxed{0.2585}
\]