Significant Figures math worksheet for practicing addition, subtraction, multiplication, division, and mixed operations with rounding to correct significant figures.

Problem: Solving the Significant Figures Worksheet

The task involves solving arithmetic problems and rounding the answers to the correct number of significant figures. Let's break it down section by section.

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Section A: Addition and Subtraction

#### Rule for Addition and Subtraction:
- The result should be rounded to the same number of decimal places as the least precise number in the calculation.

#### Problems:

1. 6.2 + 4.114 =
- Precision: 6.2 has 1 decimal place, and 4.114 has 3 decimal places.
- Result: \( 6.2 + 4.114 = 10.314 \)
- Round to 1 decimal place: 10.3

2. 19.6 - 8.77 =
- Precision: 19.6 has 1 decimal place, and 8.77 has 2 decimal places.
- Result: \( 19.6 - 8.77 = 10.83 \)
- Round to 1 decimal place: 10.8

3. 3.4 + 8.2252 =
- Precision: 3.4 has 1 decimal place, and 8.2252 has 4 decimal places.
- Result: \( 3.4 + 8.2252 = 11.6252 \)
- Round to 1 decimal place: 11.6

4. 7.8948 - 4.1 =
- Precision: 7.8948 has 4 decimal places, and 4.1 has 1 decimal place.
- Result: \( 7.8948 - 4.1 = 3.7948 \)
- Round to 1 decimal place: 3.8

5. 101.12 - 98.7 =
- Precision: 101.12 has 2 decimal places, and 98.7 has 1 decimal place.
- Result: \( 101.12 - 98.7 = 2.42 \)
- Round to 1 decimal place: 2.4

6. 23 + 16.4 + 22.0 =
- Precision: 23 has 0 decimal places, 16.4 has 1 decimal place, and 22.0 has 1 decimal place.
- Result: \( 23 + 16.4 + 22.0 = 61.4 \)
- Round to 0 decimal places: 61

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Section B: Multiplication and Division

#### Rule for Multiplication and Division:
- The result should have the same number of significant figures as the number with the fewest significant figures in the calculation.

#### Problems:

1. 1000 ÷ 8.2 =
- Significant figures: 1000 has 1 significant figure (assuming it is not a measured value), and 8.2 has 2 significant figures.
- Result: \( 1000 ÷ 8.2 = 121.9512 \)
- Round to 1 significant figure: 100 (or \( 1 \times 10^2 \) in scientific notation)

2. 10.0 × 0.02 =
- Significant figures: 10.0 has 3 significant figures, and 0.02 has 1 significant figure.
- Result: \( 10.0 × 0.02 = 0.200 \)
- Round to 1 significant figure: 0.2

3. 9.66 ÷ 0.33 =
- Significant figures: 9.66 has 3 significant figures, and 0.33 has 2 significant figures.
- Result: \( 9.66 ÷ 0.33 = 29.2727 \)
- Round to 2 significant figures: 29

4. 8000 ÷ 9.7 =
- Significant figures: 8000 has 1 significant figure (assuming it is not a measured value), and 9.7 has 2 significant figures.
- Result: \( 8000 ÷ 9.7 = 824.7423 \)
- Round to 1 significant figure: 8000 (or \( 8 \times 10^3 \) in scientific notation)

5. 0.004 × 33.511 =
- Significant figures: 0.004 has 1 significant figure, and 33.511 has 5 significant figures.
- Result: \( 0.004 × 33.511 = 0.134044 \)
- Round to 1 significant figure: 0.1

6. 0.005 × 60 =
- Significant figures: 0.005 has 1 significant figure, and 60 has 1 significant figure (assuming it is not a measured value).
- Result: \( 0.005 × 60 = 0.300 \)
- Round to 1 significant figure: 0.3

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Section C: Mixed Operation

#### Rule for Mixed Operations:
- Follow the order of operations (PEMDAS/BODMAS).
- Apply the rules for addition/subtraction and multiplication/division as needed.

#### Problems:

1. (12.3 + 0.06) × 53.44 =
- Step 1: Add \( 12.3 + 0.06 \)
- Precision: 12.3 has 1 decimal place, and 0.06 has 2 decimal places.
- Result: \( 12.3 + 0.06 = 12.36 \)
- Round to 1 decimal place: 12.4
- Step 2: Multiply \( 12.4 × 53.44 \)
- Significant figures: 12.4 has 3 significant figures, and 53.44 has 4 significant figures.
- Result: \( 12.4 × 53.44 = 663.936 \)
- Round to 3 significant figures: 664

2. 68.7 - 14.021 ÷ 18.9 =
- Step 1: Divide \( 14.021 ÷ 18.9 \)
- Significant figures: 14.021 has 5 significant figures, and 18.9 has 3 significant figures.
- Result: \( 14.021 ÷ 18.9 = 0.741899 \)
- Round to 3 significant figures: 0.742
- Step 2: Subtract \( 68.7 - 0.742 \)
- Precision: 68.7 has 1 decimal place, and 0.742 has 3 decimal places.
- Result: \( 68.7 - 0.742 = 67.958 \)
- Round to 1 decimal place: 68.0

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Final Answers:

Section A:
1. 10.3
2. 10.8
3. 11.6
4. 3.8
5. 2.4
6. 61

Section B:
1. 100
2. 0.2
3. 29
4. 8000
5. 0.1
6. 0.3

Section C:
1. 664
2. 68.0

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Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{A1: } 10.3 & \text{A2: } 10.8 \\
\text{A3: } 11.6 & \text{A4: } 3.8 \\
\text{A5: } 2.4 & \text{A6: } 61 \\
\text{B1: } 100 & \text{B2: } 0.2 \\
\text{B3: } 29 & \text{B4: } 8000 \\
\text{B5: } 0.1 & \text{B6: } 0.3 \\
\text{C1: } 664 & \text{C2: } 68.0 \\
\end{array}
}
\]