Question

Which is the best estimate for (2.8 times 10 Superscript 3 Baseline) (4.1 times 10 Superscript 6 Baseline) written in scientific notation?
7 times 10 Superscript 9
1.2 times 10 Superscript 10
1.5 times 10 Superscript 10
12 times 10 Superscript 18

Answer 1

To estimate \((2.8 \times 10^3) (4.1 \times 10^6)\) in scientific notation, we can follow these steps:

1. Multiply the coefficients (2.8 and 4.1).
2. Multiply the powers of 10.

**Step 1: Multiply the coefficients**

\[
2.8 \times 4.1 = 11.48
\]

**Step 2: Multiply the powers of 10**

\[
10^3 \times 10^6 = 10^{3+6} = 10^9
\]

**Step 3: Combine the results**

Now we combine the results:

\[
(2.8 \times 10^3)(4.1 \times 10^6) = 11.48 \times 10^9
\]

**Step 4: Convert to proper scientific notation**

In scientific notation, we want a coefficient between 1 and 10. So we need to adjust:

\[
11.48 = 1.148 \times 10^1
\]

Thus:

\[
11.48 \times 10^9 = 1.148 \times 10^1 \times 10^9 = 1.148 \times 10^{10}
\]

For estimation, we can round \(1.148\) to \(1.2\), so we can say:

\[
\approx 1.2 \times 10^{10}
\]

Therefore, the best estimate for \((2.8 \times 10^3)(4.1 \times 10^6)\) in scientific notation is:

\[
\boxed{1.2 \times 10^{10}}
\]