Significant Figures Practice Problems with Answers
Practice Problems
Significant Figures Practice Problems with Answers
Use these significant figures practice problems to test the rules you need most in chemistry, physics, and measurement-based math. The set includes counting sig figs, rounding, zeros, scientific notation, exact numbers, addition, subtraction, multiplication, and division.
Each answer includes a short explanation so you can see why the result is correct, not just copy the final number. For calculation problems, keep extra digits while working and round only at the end unless your teacher gives a different instruction.
Good sig fig practice should mix counting, rounding, operations, zeros, scientific notation, and exact numbers. Count significant digits first, identify the operation rule, keep guard digits during work, then round the final answer using either significant figures or decimal places depending on the problem type.
Significant Figures Practice Set
Work through the problems before checking the answers. In the explanations, “sig figs” means significant figures. Remember that non-zero digits count, leading zeros do not count, captive zeros count, and decimal trailing zeros count when they show measured precision.
| Problem | Answer | Why |
|---|---|---|
| How many significant figures are in 47.2? | 3 | All non-zero digits are significant. |
| How many significant figures are in 0.00450? | 3 | Leading zeros do not count; 4, 5, and the final decimal zero count. |
| How many significant figures are in 100? | Ambiguous | Whole-number trailing zeros need notation or classroom context. |
| How many significant figures are in 10.0? | 3 | The decimal point shows the zero after 10 is measured precision. |
| How many significant figures are in 5.00 × 10³? | 3 | Count the coefficient 5.00, not the power of 10. |
| Round 0.07849 to 2 sig figs. | 0.078 | The first two significant digits are 7 and 8; the next digit is 4. |
| Round 9.876 to 3 sig figs. | 9.88 | The first three significant digits are 9, 8, and 7; the next digit rounds up. |
| 12.4 + 3.15 | 15.6 | Addition is rounded by decimal places; 12.4 has one decimal place. |
| 18.62 – 4.1 | 14.5 | Subtraction is rounded by decimal places; 4.1 has one decimal place. |
| 6.20 × 3.1 | 19 | Multiplication is rounded to the fewest sig figs; 3.1 has 2 sig figs. |
| 45.0 ÷ 2.50 | 18.0 | Both values have 3 sig figs, so the quotient needs 3 sig figs. |
| Counted 12 students measured 4.52 g each. Total mass? | 54.2 g | The 12 students is an exact counted number, so 4.52 limits the answer to 3 sig figs. |
Counting Sig Figs: Practice Explanations
Counting problems are often about zeros. Leading zeros only locate the decimal point, so they do not add precision. Zeros between non-zero digits are always significant. Zeros at the end of a decimal number are significant because they show the measurement was recorded to that place.
Rounding Practice Problems
When rounding to significant figures, start counting at the first non-zero digit. Keep the requested number of significant digits, then look at the next digit to decide whether to round up or stay the same.
| Original Number | Instruction | Rounded Answer |
|---|---|---|
| 456.7 | 2 sig figs | 460 |
| 0.003684 | 3 sig figs | 0.00368 |
| 91.05 | 3 sig figs | 91.1 |
| 7.995 | 3 sig figs | 8.00 |
| 1200 | 2 sig figs | 1.2 × 10³ |
Operations Practice: Addition, Subtraction, Multiplication, and Division
The operation decides the rounding rule. Addition and subtraction use decimal places, not total significant figures. Multiplication and division use the number of significant figures in the least precise input.
Addition and Subtraction
For addition and subtraction, line up the decimal places and round the final answer to the least number of decimal places shown by the measured values.
Multiplication and Division
For multiplication and division, first calculate the result, then round it to the same number of significant figures as the measured input with the fewest sig figs.
Scientific Notation Practice
Scientific notation makes precision clearer because the coefficient shows the significant figures. The exponent tells you the size of the number, but it does not change how many sig figs are present.
| Number | Sig Figs | Explanation |
|---|---|---|
| 6.02 × 10²³ | 3 | Only the coefficient 6.02 is counted. |
| 1.230 × 10⁻⁴ | 4 | The final zero in 1.230 is significant. |
| 7.0 × 10³ | 2 | The decimal zero in 7.0 shows precision. |
Exact Numbers Practice
Exact counted numbers and defined conversion factors usually do not limit significant figures. For example, 12 eggs, 4 students, and exactly 100 cm in 1 m are not measured estimates in the usual classroom sense.
Common Mistakes in Sig Fig Practice
Most wrong answers come from choosing the wrong rounding rule or misreading zeros. These are the mistakes to check before you submit homework or lab calculations.
| Mistake | Why It Happens | Better Habit |
|---|---|---|
| Counting leading zeros | They look like digits, but they only place the decimal. | Start counting at the first non-zero digit. |
| Rounding addition by sig figs | Students mix up operation rules. | Use decimal places for addition and subtraction. |
| Rounding too early | Intermediate answers look cleaner. | Keep guard digits and round the final result. |
| Treating 100 as always 1 sig fig | Whole-number trailing zeros are easy to oversimplify. | Check notation, decimal point, or teacher convention. |
Practical Tips for Practicing Sig Figs
For faster practice, label the rule before solving. Write “counting,” “rounding,” “add/subtract,” or “multiply/divide” beside each problem. This prevents you from using the wrong rule on mixed worksheets.
When to Use SigFigLab
Use the SigFigLab Sig Fig Calculator after you try the problems by hand. It is most helpful for checking counts, testing rounded answers, and confirming whether zeros or scientific notation are being interpreted the way you expect.
FAQs
What are significant figures practice problems?
They are problems that test how to count meaningful digits, round measured values, and apply precision rules in calculations.
How do I know how many sig figs are in a number?
Start at the first non-zero digit, count all non-zero digits, count zeros between non-zero digits, and count trailing zeros after a decimal point.
Do leading zeros count as significant figures?
No. Leading zeros before the first non-zero digit do not count because they only show decimal placement.
Why is 100 sometimes ambiguous?
In a whole number without a decimal point, trailing zeros may or may not show measured precision. Scientific notation or classroom context can clarify it.
What rule should I use for addition and subtraction?
Round the answer by decimal places. The result should match the least precise decimal place among the measured inputs.
What rule should I use for multiplication and division?
Round the answer to the same number of significant figures as the input with the fewest significant figures.
Do exact numbers limit significant figures?
Usually no. Counted quantities and defined conversion factors normally do not limit the final answer’s significant figures.
Should I round during each step of a long calculation?
Usually you should not round too early. Keep extra guard digits during the calculation and round the final result unless your teacher says otherwise.
Check Your Work After Practicing
Try solving the problems by hand first, then compare your answers with a sig fig checker. That habit helps you learn the rules instead of depending on the final answer alone.