To solve the multiplication \( 45.20 \times 0.0071 \), we will follow these steps: perform the calculation, identify the number of significant figures in each number, and then round the final answer to the correct number of significant figures.
Step 1: Perform the Calculation
Using a calculator:
\[ 45.20 \times 0.0071 = 0.32192 \]
Step 2: Identify the Number of Significant Figures
Now, we need to determine the number of significant figures in each number.
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For 45.20:
- The number has 4 significant figures. The trailing zero after the decimal point counts as significant.
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For 0.0071:
- The number has 2 significant figures. The leading zeros do not count, but both non-zero digits (7 and 1) do.
Step 3: Rounding to the Correct Number of Significant Figures
When multiplying, the result should be rounded to the least number of significant figures present in the numbers being multiplied. Here, 0.0071 has the fewest significant figures (2).
The intermediate result from the calculation is:
\[ 0.32192 \]
Step 4: Rounding
We will round \( 0.32192 \) to 2 significant figures:
- The first two significant figures of \( 0.32192 \) are 3 and 2.
- The next digit (1) tells us to round down, so we keep the 2.
Thus, rounding \( 0.32192 \) to 2 significant figures gives us \( 0.32 \).
Final Result
- Calculator answer: \( 0.32192 \)
- Final answer with significant figures: \( 0.32 \)
- Number of significant figures in the final answer: 2
In summary:
- \( 45.20 \times 0.0071 = 0.32192 \)
- Rounded answer: \( 0.32 \) (2 significant figures)