Significant Figures Worksheet for 15-Year-Olds — Math Practice & Examples

Instructions

Significant figures (or "sig figs") are the digits in a number that are reliable and necessary to indicate the quantity of something. They are important in science and math to show the precision of a measurement. Please read the rules recap below and complete the exercises.

Significant Figures Rules Recap:

• Rule 1: Non-zero digits are always significant. (e.g., 123 has 3 sig figs)
• Rule 2: Zeros between non-zero digits are significant. (e.g., 101 has 3 sig figs)
• Rule 3: Leading zeros (zeros before non-zero digits) are not significant. (e.g., 0.085 has 2 sig figs)
• Rule 4: Trailing zeros (zeros at the end) are significant only if the number contains a decimal point. (e.g., 85.0 has 3 sig figs, but 8500 has only 2)

Rules for Calculations:

• Multiplication & Division: The result should have the same number of significant figures as the measurement with the least number of significant figures.
• Addition & Subtraction: The result should have the same number of decimal places as the measurement with the least number of decimal places.

Part 1: How Many Significant Figures?

Determine the number of significant figures in each of the following numbers.

1. 405
2. 22.0
3. 0.0091
4. 31,000
5. 901.0
6. 1.004
7. 0.05060
8. 6.20 x 10⁴

Part 2: Rounding with Significant Figures

Round each of the following numbers to the specified number of significant figures.

1. Round 54.882 to 3 significant figures.
2. Round 0.007639 to 2 significant figures.
3. Round 1,255,000 to 2 significant figures.
4. Round 99.96 to 3 significant figures.

Part 3: Calculations with Significant Figures

Perform the following calculations and round your answer to the correct number of significant figures.

1. 8.2 cm × 1.5 cm =
2. 25.0 g ÷ 5.00 mL =
3. 15.75 m + 2.1 m =
4. 189.55 s - 12.3 s =
5. (5.15 × 10³) × (2.8 × 10²) =
6. 98.11 kg + 2.0 kg + 0.94 kg =

Part 4: Word Problems

Solve the following problems, making sure to use the correct number of significant figures in your final answer.

1. A student measures the sides of a rectangular piece of paper to be 21.5 cm and 27.94 cm. What is the area of the paper? (Area = length × width)
2. To find the density of a rock, you measure its mass to be 45.2 g and its volume to be 15.0 cm³. What is the density of the rock? (Density = mass / volume)

Answer Key

Part 1: How Many Significant Figures?

1. 3 (Zeros between non-zeros are significant)
2. 3 (Trailing zeros are significant if there is a decimal point)
3. 2 (Leading zeros are not significant)
4. 2 (Trailing zeros in a whole number are not significant)
5. 4 (Zero between non-zeros and trailing zero with a decimal are both significant)
6. 4 (Zero between non-zeros is significant)
7. 4 (Leading zeros are not significant; the captive zero and trailing zero are)
8. 3 (For scientific notation, only look at the coefficient)

Part 2: Rounding with Significant Figures

1. 54.9
2. 0.0076
3. 1,300,000
4. 100. (or 1.00 x 10² to be unambiguous)

Part 3: Calculations with Significant Figures

1. 12 cm² (Raw answer is 12.3. 8.2 has 2 sig figs, so the answer is rounded to 2 sig figs.)
2. 5.00 g/mL (Raw answer is 5. 25.0 and 5.00 both have 3 sig figs, so the answer must have 3.)
3. 17.9 m (Raw answer is 17.85. For addition, round to the least number of decimal places. 2.1 m has one decimal place.)
4. 177.3 s (Raw answer is 177.25. For subtraction, round to the least number of decimal places. 12.3 s has one decimal place.)
5. 1.4 × 10⁶ (Raw answer is 1,442,000. 2.8 has 2 sig figs, so the answer must be rounded to 2 sig figs.)
6. 101.1 kg (Raw answer is 101.05. For addition, round to the least number of decimal places. 2.0 kg has one decimal place.)

Part 4: Word Problems

1. 601 cm² (Calculation: 21.5 cm × 27.94 cm = 600.61 cm². The measurement 21.5 cm has the least number of significant figures (3), so the answer is rounded to 3 significant figures.)
2. 3.01 g/cm³ (Calculation: 45.2 g ÷ 15.0 cm³ = 3.0133... g/cm³. Both measurements have 3 significant figures, so the answer is rounded to 3 significant figures.)