Significant Figures Worksheet for 15-Year-Olds — High School Math Practice

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Instructions

This worksheet will help you practice working with significant figures (often called "sig figs"). Significant figures are the digits in a number that are reliable and necessary to indicate the quantity of something. First, review the rules, then complete the exercises that follow. Show your work for the calculation problems.

Summary of Rules for Significant Figures

  • Rule 1: Non-zero digits (1, 2, 3, 4, 5, 6, 7, 8, 9) are always significant.
  • Rule 2: Zeros sandwiched between non-zero digits are always significant (e.g., in 707, the zero is significant).
  • Rule 3: Leading zeros (zeros at the beginning) are never significant (e.g., in 0.005, the zeros are not significant).
  • Rule 4: Trailing zeros (zeros at the end) are significant only if the number contains a decimal point (e.g., in 5.00 the zeros are significant, but in 500 they are not).
  • Scientific Notation: All digits in the coefficient of a number in scientific notation are significant (e.g., 6.02 x 10²³ has 3 significant figures).

Part 1: Identifying Significant Figures

For each number below, state how many significant figures it contains.

  1. 1,234
  2. 90,800
  3. 0.00056
  4. 7.200
  5. 101.01
  6. 3.40 x 10⁴
  7. 500
  8. 8,000.0

Part 2: Rounding Practice

Round each number to the specified number of significant figures.

  1. Round 84,572 to 3 significant figures:
  2. Round 0.02589 to 2 significant figures:
  3. Round 99.95 to 3 significant figures:
  4. Round 4.008 to 2 significant figures:

Part 3: Calculations with Significant Figures

Solve the following problems. Make sure your final answer has the correct number of significant figures.

A. Addition & Subtraction
Rule: Your answer must be rounded to the same number of decimal places as the measurement with the fewest decimal places.

  1. 12.52 cm + 349.0 cm + 8.24 cm =
  2. 75.5 m - 0.55 m =
  3. 13.75 g + 2.1 g =

B. Multiplication & Division
Rule: Your answer must be rounded to the same number of significant figures as the measurement with the fewest significant figures.

  1. 5.28 m * 1.5 m =
  2. 28.0 g / 4.115 mL =
  3. (18.2 cm * 4.6 cm) / 2.54 cm =

Part 4: Challenge Problem

A student measures the mass of a rock to be 150.3 grams. They then place the rock into a graduated cylinder containing water, and the volume of the rock is found to be 21.5 mL. Calculate the density of the rock (Density = Mass / Volume). Express your final answer with the correct number of significant figures.

Answer Key

Part 1 Answers

  1. 4
  2. 3
  3. 2
  4. 4
  5. 5
  6. 3
  7. 1
  8. 5

Part 2 Answers

  1. 84,600
  2. 0.026
  3. 100. (The decimal is required to show 3 sig figs)
  4. 4.0

Part 3 Answers

A. Addition & Subtraction

  1. Calculator answer: 369.76 cm. Final Answer: 369.8 cm (rounded to one decimal place).
  2. Calculator answer: 74.95 m. Final Answer: 75.0 m (rounded to one decimal place).
  3. Calculator answer: 15.85 g. Final Answer: 15.9 g (rounded to one decimal place).

B. Multiplication & Division

  1. Calculator answer: 7.92 m². Final Answer: 7.9 m² (rounded to 2 sig figs).
  2. Calculator answer: 6.804374... g/mL. Final Answer: 6.80 g/mL (rounded to 3 sig figs).
  3. Calculator answer: 33.022... cm. Final Answer: 33 cm (rounded to 2 sig figs from 4.6).

Part 4 Answer

Calculation: 150.3 g / 21.5 mL = 6.99069... g/mL
The mass (150.3) has 4 significant figures. The volume (21.5) has 3 significant figures. The answer must be rounded to the least number of significant figures, which is 3.
Final Answer: 6.99 g/mL

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