Question

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



0.00026 0.00026 0.0026 0.0026 0.26 0.26 2.6

Answer 1

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

1. **Multiply the first two terms:**
\[
(3.2 \times 4.2) \times (10^{-2} \times 10^{6}) = 13.44 \times 10^{4}
\]

Here, \(10^{-2} \times 10^{6} = 10^{(-2+6)} = 10^{4}\).

2. **Now, divide by the third term:**
\[
\frac{13.44 \times 10^{4}}{5.2 \times 10^{5}} = \frac{13.44}{5.2} \times \frac{10^{4}}{10^{5}}
\]

For the powers of ten:
\[
\frac{10^{4}}{10^{5}} = 10^{(4-5)} = 10^{-1}
\]

3. **Now, calculate \(\frac{13.44}{5.2}\):**
\[
\frac{13.44}{5.2} \approx 2.58
\]

So, we have:
\[
2.58 \times 10^{-1}
\]

4. **Convert to standard notation:**
\[
2.58 \times 10^{-1} = 0.258
\]

None of the answer choices correspond exactly, but it seems there was a slight miscalculation earlier. Let's verify:

If we divide 13.44 by 5.2 more carefully:
\[
\frac{13.44}{5.2} \approx 2.58 \text{ is correct.}
\]

Thus, \(2.58 \times 10^{-1} = 0.258\).

Given the options provided (0.00026, 0.0026, 0.26, 2.6), the closest answer (if we round appropriately) would be **0.26**.

So the answer is:
\[
\boxed{0.26}
\]