Q1. Calculate: 28.4445 + 42.7 + 0.259 = ____________

Background

Topic: Significant Figures in Addition

This question tests your understanding of how to add numbers and report the answer with the correct number of decimal places based on significant figures.

Key Terms and Formulas:

• Significant Figures (sig figs): The digits in a number that are meaningful in terms of accuracy.

• Rule for Addition/Subtraction: The answer should have the same number of decimal places as the measurement with the fewest decimal places.

Step-by-Step Guidance

1. Identify the number of decimal places in each number: 28.4445 (4 dp), 42.7 (1 dp), 0.259 (3 dp).

2. Add the numbers together: .

3. Determine which number has the fewest decimal places (1 dp in 42.7).

4. Round your sum to 1 decimal place.

Try solving on your own before revealing the answer!

Q2. Calculate: 5.159 + 82.3 + 0.024 - 3.00 = ____________

Background

Topic: Significant Figures in Addition and Subtraction

This question tests your ability to apply significant figure rules to a series of additions and subtractions.

Key Terms and Formulas:

• Significant Figures: Focus on decimal places for addition/subtraction.

• Rule: The result should have the same number of decimal places as the least precise measurement.

Step-by-Step Guidance

1. List the decimal places: 5.159 (3 dp), 82.3 (1 dp), 0.024 (3 dp), 3.00 (2 dp).

2. Add and subtract in sequence: .

3. Identify the number with the fewest decimal places (82.3, 1 dp).

4. Round your final result to 1 decimal place.

Try solving on your own before revealing the answer!

Q3. Calculate: 2.404 + 9.848 × 5.928 - 5.434 = ____________

Background

Topic: Significant Figures in Mixed Operations

This question tests your ability to apply significant figure rules to a calculation involving both multiplication and addition/subtraction.

Key Terms and Formulas:

• Multiplication/Division: The answer should have the same number of significant figures as the value with the fewest sig figs.

• Add/Subtract: The answer should have the same number of decimal places as the value with the fewest decimal places.

Step-by-Step Guidance

1. First, multiply (both have 4 sig figs).

2. Round the product to 4 significant figures.

3. Add to the rounded product.

4. Subtract from the sum.

5. Round the final answer to the correct number of decimal places (based on the least precise decimal place in the addition/subtraction steps).

Try solving on your own before revealing the answer!

Q4. Calculate: 2.404 + 9.848 × 5.928 - 5.434 = ____________ (alternate setup)

Background

Topic: Significant Figures in Mixed Operations

This is a similar question to Q3, but may involve a different order of operations or grouping.

Key Terms and Formulas:

• Order of Operations: Perform multiplication before addition/subtraction.

• Significant Figures: Apply rules for multiplication and addition/subtraction as appropriate.

Step-by-Step Guidance

1. Multiply (both have 4 sig figs).

2. Round the product to 4 significant figures.

3. Add to the rounded product.

4. Subtract from the sum.

5. Round the final answer to the correct number of decimal places.

Try solving on your own before revealing the answer!

Q5. Calculate: (2.349 × 31.39) × (4.909 - 4.354) = ____________

Background

Topic: Significant Figures in Multiplication and Subtraction

This question tests your ability to apply significant figure rules to a calculation involving both multiplication and subtraction.

Key Terms and Formulas:

• Multiplication/Division: The answer should have the same number of significant figures as the value with the fewest sig figs.

• Subtraction: The answer should have the same number of decimal places as the value with the fewest decimal places.

Step-by-Step Guidance

1. Subtract (both have 3 decimal places).

2. Multiply (both have 4 sig figs).

3. Multiply the result of the subtraction by the result of the multiplication.

4. Round the final answer to the correct number of significant figures (based on the value with the fewest sig figs).

Try solving on your own before revealing the answer!

Q6. Calculate: -27.89 ÷ 2.2683 - 1.791 + 52.865 = ____________

Background

Topic: Significant Figures in Division, Addition, and Subtraction

This question tests your ability to apply significant figure rules to a calculation involving division, subtraction, and addition.

Key Terms and Formulas:

• Division: The answer should have the same number of significant figures as the value with the fewest sig figs.

• Add/Subtract: The answer should have the same number of decimal places as the value with the fewest decimal places.

Step-by-Step Guidance

1. Divide (both have 4 sig figs).

2. Subtract from the result.

3. Add to the result.

4. Round the final answer to the correct number of decimal places or significant figures, as appropriate.

Try solving on your own before revealing the answer!