Practice worksheet for significant figures in multiplication and division.

Problem Description:

The task involves solving a series of multiplication and division problems while adhering to the rules of significant figures. The results must be rounded to the correct number of significant figures based on the given inputs.

Rules for Significant Figures:

1. Multiplication and Division: The result should have the same number of significant figures as the number with the fewest significant figures in the calculation.
2. Addition and Subtraction: The result should be rounded to the same decimal place as the number with the fewest decimal places in the calculation.

Solution:

#### 1. \( 6 \times 0.30 \)
- \( 6 \) has 1 significant figure.
- \( 0.30 \) has 2 significant figures.
- Result: \( 6 \times 0.30 = 1.8 \) (round to 1 significant figure).
- Answer: \( 2 \)

#### 2. \( 0.53 \times 7 \times 210 \)
- \( 0.53 \) has 2 significant figures.
- \( 7 \) has 1 significant figure.
- \( 210 \) has 2 significant figures (assuming trailing zeros are not significant unless specified otherwise).
- Result: \( 0.53 \times 7 \times 210 = 779.1 \) (round to 1 significant figure).
- Answer: \( 800 \) (or \( 8 \times 10^2 \))

#### 3. \( 11.6 \div 8.24 \)
- \( 11.6 \) has 3 significant figures.
- \( 8.24 \) has 3 significant figures.
- Result: \( 11.6 \div 8.24 = 1.40776 \) (round to 3 significant figures).
- Answer: \( 1.41 \)

#### 4. \( 0.0045 \times 2000 \)
- \( 0.0045 \) has 2 significant figures.
- \( 2000 \) has 1 significant figure (assuming no trailing zeros are significant).
- Result: \( 0.0045 \times 2000 = 9 \) (round to 1 significant figure).
- Answer: \( 9 \)

#### 5. \( 500.95 \times 8.11 \)
- \( 500.95 \) has 5 significant figures.
- \( 8.11 \) has 3 significant figures.
- Result: \( 500.95 \times 8.11 = 4070.0445 \) (round to 3 significant figures).
- Answer: \( 4070 \) (or \( 4.07 \times 10^3 \))

#### 6. \( 1000 \div 8.3 \)
- \( 1000 \) has 1 significant figure (assuming no trailing zeros are significant).
- \( 8.3 \) has 2 significant figures.
- Result: \( 1000 \div 8.3 = 120.4819 \) (round to 1 significant figure).
- Answer: \( 100 \)

#### 7. \( 5.16 \times 31.4 \)
- \( 5.16 \) has 3 significant figures.
- \( 31.4 \) has 3 significant figures.
- Result: \( 5.16 \times 31.4 = 161.904 \) (round to 3 significant figures).
- Answer: \( 162 \)

#### 8. \( 8080 \times 3.4 \)
- \( 8080 \) has 3 significant figures.
- \( 3.4 \) has 2 significant figures.
- Result: \( 8080 \times 3.4 = 27472 \) (round to 2 significant figures).
- Answer: \( 27000 \) (or \( 2.7 \times 10^4 \))

#### 9. \( 204.17 \div 2.42 \)
- \( 204.17 \) has 5 significant figures.
- \( 2.42 \) has 3 significant figures.
- Result: \( 204.17 \div 2.42 = 84.36777 \) (round to 3 significant figures).
- Answer: \( 84.4 \)

#### 10. \( 31.2 \times 4.1 \)
- \( 31.2 \) has 3 significant figures.
- \( 4.1 \) has 2 significant figures.
- Result: \( 31.2 \times 4.1 = 127.92 \) (round to 2 significant figures).
- Answer: \( 130 \)

#### 11. \( 8000 \div 9.7 \)
- \( 8000 \) has 1 significant figure (assuming no trailing zeros are significant).
- \( 9.7 \) has 2 significant figures.
- Result: \( 8000 \div 9.7 = 824.7423 \) (round to 1 significant figure).
- Answer: \( 8000 \) (or \( 8 \times 10^3 \))

#### 12. \( 35.45 \div 6.1 \)
- \( 35.45 \) has 4 significant figures.
- \( 6.1 \) has 2 significant figures.
- Result: \( 35.45 \div 6.1 = 5.811475 \) (round to 2 significant figures).
- Answer: \( 5.8 \)

#### 13. \( 1.1 \times 3.25 \)
- \( 1.1 \) has 2 significant figures.
- \( 3.25 \) has 3 significant figures.
- Result: \( 1.1 \times 3.25 = 3.575 \) (round to 2 significant figures).
- Answer: \( 3.6 \)

#### 14. \( 1200 \div 19.7 \)
- \( 1200 \) has 2 significant figures (assuming no trailing zeros are significant).
- \( 19.7 \) has 3 significant figures.
- Result: \( 1200 \div 19.7 = 60.9137 \) (round to 2 significant figures).
- Answer: \( 61 \)

#### 15. \( 10.2 \div 9.02 \)
- \( 10.2 \) has 3 significant figures.
- \( 9.02 \) has 3 significant figures.
- Result: \( 10.2 \div 9.02 = 1.13082 \) (round to 3 significant figures).
- Answer: \( 1.13 \)

#### 16. \( 6800 \div 2.4 \)
- \( 6800 \) has 2 significant figures (assuming no trailing zeros are significant).
- \( 2.4 \) has 2 significant figures.
- Result: \( 6800 \div 2.4 = 2833.3333 \) (round to 2 significant figures).
- Answer: \( 2800 \) (or \( 2.8 \times 10^3 \))

#### 17. \( 3.3 \div 2.7 \)
- \( 3.3 \) has 2 significant figures.
- \( 2.7 \) has 2 significant figures.
- Result: \( 3.3 \div 2.7 = 1.22222 \) (round to 2 significant figures).
- Answer: \( 1.2 \)

#### 18. \( 31.86 \div 0.02 \)
- \( 31.86 \) has 4 significant figures.
- \( 0.02 \) has 1 significant figure.
- Result: \( 31.86 \div 0.02 = 1593 \) (round to 1 significant figure).
- Answer: \( 2000 \) (or \( 2 \times 10^3 \))

#### 19. \( 2.98 \div 0.33 \)
- \( 2.98 \) has 3 significant figures.
- \( 0.33 \) has 2 significant figures.
- Result: \( 2.98 \div 0.33 = 9.0303 \) (round to 2 significant figures).
- Answer: \( 9.0 \)

#### 20. \( 12.4 \times 12.8 \times 16 \)
- \( 12.4 \) has 3 significant figures.
- \( 12.8 \) has 3 significant figures.
- \( 16 \) has 2 significant figures.
- Result: \( 12.4 \times 12.8 \times 16 = 2508.8 \) (round to 2 significant figures).
- Answer: \( 2500 \) (or \( 2.5 \times 10^3 \))

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 2 \\
2. & 800 \\
3. & 1.41 \\
4. & 9 \\
5. & 4070 \\
6. & 100 \\
7. & 162 \\
8. & 27000 \\
9. & 84.4 \\
10. & 130 \\
11. & 8000 \\
12. & 5.8 \\
13. & 3.6 \\
14. & 61 \\
15. & 1.13 \\
16. & 2800 \\
17. & 1.2 \\
18. & 2000 \\
19. & 9.0 \\
20. & 2500 \\
\end{array}
}
\]