Question

Estimate the following product in scientific notation, and then select the best answer for the product’s power of 10. (8.91 x 10power of 2) (3.3 x 10power of 12) 2.7 14 15 27

Answer 1

To estimate the product \((8.91 \times 10^2) (3.3 \times 10^{12})\), we can break it down into two parts: the coefficients and the powers of 10.

1. **Multiply the coefficients:**
\[
8.91 \times 3.3 \approx 29.43
\]
For estimation, we can approximate this to \(30\).

2. **Add the exponents of 10:**
\[
10^2 \times 10^{12} = 10^{(2+12)} = 10^{14}
\]

Now combining both parts, we get:
\[
30 \times 10^{14}
\]

Since we want the product in scientific notation, we convert \(30\) to \(3.0 \times 10^1\):
\[
(3.0 \times 10^1) \times 10^{14} = 3.0 \times 10^{(1 + 14)} = 3.0 \times 10^{15}
\]

Thus, the estimated product is \(3.0 \times 10^{15}\).

The power of 10 for the product is \(15\).

So, the best answer for the product’s power of 10 is **15**.