Questions: How many significant figures would this calculation have if it were completed: (9.04-8.23+21.954+81.0) × 3.1416 A 3 B 4 C 5 D 6

How many significant figures would this calculation have if it were completed: (9.04-8.23+21.954+81.0) × 3.1416 A 3 B 4 C 5 D 6
Transcript text: How many significant figures would this calculation have if it were completed: \[ (9.04-8.23+21.954+81.0) \times 3.1416 \] A \[ 3 \] B \[ 4 \] C \[ 5 \] D 6
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Solution

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Solution Steps

To determine the number of significant figures in the result of the given calculation, we need to follow these steps:

  1. Perform the addition and subtraction inside the parentheses.
  2. Identify the number of significant figures in the result of the parentheses.
  3. Multiply the result by 3.1416.
  4. Determine the number of significant figures in the final result based on the least number of significant figures in the intermediate results.
Step 1: Perform the Addition and Subtraction Inside the Parentheses

First, we calculate the expression inside the parentheses: \[ 9.04 - 8.23 + 21.954 + 81.0 = 103.764 \]

Step 2: Identify the Number of Significant Figures in the Intermediate Result

The least number of decimal places in the terms inside the parentheses is 1 (from \(81.0\)). Therefore, the intermediate result \(103.764\) should be rounded to one decimal place: \[ 103.764 \approx 103.8 \]

Step 3: Multiply the Intermediate Result by 3.1416

Next, we multiply the rounded intermediate result by \(3.1416\): \[ 103.8 \times 3.1416 = 325.9849824 \]

Step 4: Determine the Number of Significant Figures in the Final Result

The least number of significant figures in the multiplication is 4 (from \(3.1416\)). Therefore, the final result should be rounded to 4 significant figures: \[ 325.9849824 \approx 326.0 \]

Final Answer

\(\boxed{4}\)

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