Sig fig rules
| Rule | Example | Sig figs |
|---|---|---|
| Nonzero digits are significant | 123.45 | 5 |
| Zeros between nonzero digits are significant | 1002 | 4 |
| Leading zeros are not significant | 0.0045 | 2 |
| Trailing zeros after a decimal point are significant | 2.500 | 4 |
| Trailing zeros in a whole number are ambiguous | 1500 | 2 to 4 |
| A trailing decimal point makes the zeros significant | 1500. | 4 |
| Scientific notation shows only the significant digits | 1.50 × 10^3 | 3 |
| Exact counts have unlimited sig figs | 12 eggs | Unlimited |
Sig fig arithmetic problems
For addition and subtraction, round the answer to the fewest decimal places in the data.
For multiplication and division, round the answer to the fewest significant figures in the data.
Keep all digits during intermediate steps. Round only the final answer.
Problem 1
Add 12.11 + 18.0 + 1.013.
- The unrounded sum is 31.123.
- 18.0 has the fewest decimal places: one.
- Round the sum to one decimal place.
Answer: 31.1
Problem 2
Multiply 4.56 × 1.4.
- The unrounded product is 6.384.
- 1.4 has the fewest significant figures: two.
- Round the product to two significant figures.
Answer: 6.4
Problem 3
Subtract 100.0 − 9.87.
- The unrounded difference is 90.13.
- 100.0 has one decimal place, and 9.87 has two.
- Round the difference to one decimal place.
Answer: 90.1
Problem 4
Divide 9.0 ÷ 3.000.
- The unrounded quotient is 3.
- 9.0 has two significant figures, and 3.000 has four.
- Write the answer with two significant figures.
Answer: 3.0
Problem 5
Round 0.0045678 to three sig figs.
- Skip the leading zeros. The first significant digit is 4.
- Keep 4, 5, and 6. The next digit is 7, so round the 6 up to 7.
Answer: 0.00457
How to use this calculator
- Select a mode: count, round, add, subtract, multiply, divide, or scientific.
- Enter one value or a comma-separated list.
- Enter the number of sig figs when you round or format a value.
- Calculate and read the answer and any ambiguity warning.
Formula and variables
addition/subtraction: least decimal places; multiplication/division: fewest significant figures
| Symbol | Meaning | Unit |
|---|---|---|
| sf | significant figures | digits |
Worked example
0.00450 has three significant figures; 1500 is ambiguous; 1500. and 1.500e3 explicitly have four.
Interpretation
The parser preserves how a value was written so trailing decimal points and scientific notation remain meaningful.
Common mistakes
- Do not assume trailing whole-number zeros are significant without notation.
- Use comma-separated values only for arithmetic modes.
Frequently asked questions
What does a sig fig solver do?
It counts significant figures, rounds values, and applies sig fig rules to arithmetic answers.
How many sig figs are in 0.50?
0.50 has two significant figures. The leading zero is not significant, and the trailing zero after the decimal point is significant.
How many sig figs are in 500?
500 is ambiguous. Most textbooks count one significant figure. Write 500. for three or 5.0e2 for two.
Are leading zeros significant?
No. Leading zeros locate the decimal point and do not count as significant figures.
Are trailing zeros significant?
Trailing zeros after a decimal point are significant. Trailing whole-number zeros can be ambiguous.
Which rule applies to arithmetic?
Addition and subtraction use decimal places. Multiplication and division use significant figures.
Can I use scientific notation?
Yes. Enter values such as 6.022e23 or 1.0e-6 in a numeric field.
How should I round the result?
Keep extra digits during the calculation. Round the final result to the precision required by your data.