To perform the multiplication \( 25.7 \times 0.78 \times 2.3 \), we'll calculate the answer step by step and determine the significant figures in the final result.
Step 1: Calculate using a calculator
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Calculate \( 25.7 \times 0.78 \): \[ 25.7 \times 0.78 = 20.046 \]
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Multiply the result by \( 2.3 \): \[ 20.046 \times 2.3 = 46.1058 \]
Step 2: Identify significant figures
Now, we will identify the number of significant figures in each of the original numbers:
- 25.7: 3 significant figures (the digits 2, 5, and 7)
- 0.78: 2 significant figures (the digits 7 and 8)
- 2.3: 2 significant figures (the digits 2 and 3)
Step 3: Determine the limiting factor
When multiplying numbers, the result should have the same number of significant figures as the number with the fewest significant figures.
- \( 25.7 \) has 3 significant figures
- \( 0.78 \) has 2 significant figures (limiting factor)
- \( 2.3 \) has 2 significant figures
Thus, our final result will be limited to 2 significant figures.
Step 4: Round the answer
The calculator answer from our multiplication was 46.1058. To round this to 2 significant figures:
- Look at the first two digits (46).
- The next digit (1) indicates we do not need to round up.
Thus, rounding \( 46.1058 \) to 2 significant figures gives us 46.
Final Summary:
- Calculator answer: \( 46.1058 \)
- Significant digits answer: \( 46 \)
- Number of significant digits: 2
So the final answer is 46 with 2 significant figures.