Significant figures calculator (count, round and calculate)
Enter your values. The answer and the full worked solution update as you type.
Result
Count the significant figures of a number, round a number to a chosen number of significant figures, or calculate with two measured values and round the answer by the rules for significant figures. The calculator marks which digits count and explains each rule, including the ambiguous trailing zeros of whole numbers such as 1200.
Step-by-step solution
Apply the rules digit by digit
Scientific notation shows them clearly
Key formulas
- Multiplying and dividing
- keep as many significant figures as the input with the fewest
- Adding and subtracting
- keep as many decimal places as the input with the fewest
- Rounding
- look at the first digit you drop: 5 or more rounds up
- Zeros
- leading zeros never count; trailing zeros count after a decimal point
How to count significant figures
- Every non-zero digit is significant: 4.56 has three significant figures.
- Zeros between non-zero digits are significant: 1005 has four.
- Leading zeros are never significant; they only place the decimal point: 0.0045 has two.
- Trailing zeros are significant when the number has a decimal point: 2.500 has four and 1200. has four. Without a decimal point, as in 1200, they are ambiguous and usually not counted.
- In scientific notation every digit of the coefficient is significant: 1.20 × 10³ has three.
- When calculating: for × and ÷ keep as many significant figures as the value with the fewest; for + and − round to the last decimal place that both values have.
Questions and answers
How many significant figures does 100 have?
It is ambiguous: one, two or three. Without more information it is usually read as one. Write 1.00 × 10², or 100. with a decimal point, to show three significant figures.
Why are the rules for adding different from the rules for multiplying?
When you add, absolute uncertainties combine, so the least precise decimal place limits the result: 12.52 + 1.1 = 13.6. When you multiply, relative uncertainties combine, so the number of significant figures limits it: 12.52 × 1.1 = 14.
Do exact numbers limit the significant figures?
No. Counted numbers, such as 3 apples, and defined factors, such as 100 cm in 1 m, are exact and have unlimited significant figures.
How do I round 2.45 to two significant figures?
Look at the first dropped digit: it is 5, so round up to 2.5. This calculator uses the common rule of rounding a 5 up. Some fields round an exact 5 to the nearest even digit instead, which would give 2.4.
Should I round in the middle of a calculation?
No. Keep all digits in intermediate steps and round only the final answer, otherwise the rounding errors add up.
Practise it yourself
Practise Descriptive statistics
A calculator gives the answer. In the exam you need the method: practise it with new problems, hints and worked solutions.