About Significant Figures Addition
This calculator adds and subtracts measured numbers and rounds the answer by the sig fig rule for addition: keep as many decimal places as the least precise number. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The page opens on 12.11 + 1.013. The exact sum is 13.123. The first number is known to the hundredths place and the second to the thousandths, so the answer is rounded to the hundredths: 13.12. Counting significant figures would give a different, wrong answer, because addition is about decimal places.
Subtraction works the same way: 150.2 - 3.456 = 146.744 exactly, and since 150.2 is known only to the tenths place the answer is 146.7.
How to use Significant Figures Addition
- Choose Count, Round, Arithmetic or Scientific notation.
- Type the number exactly as it was measured, keeping any trailing zeros: 0.00450, 1200, 1.20e3.
- For rounding, set how many significant figures to keep. For arithmetic, type the second number and choose the operation.
- Read the answer, then open the digit-by-digit reasons or the steps.
- For a whole number that ends in zeros, use the switch to say whether those zeros were measured.
Features
- Digit-by-digit rule explanation: leading, non-zero, captive and trailing zeros.
- Round to any number of significant figures from 1 to 50, half up.
- Add and subtract by decimal places, multiply and divide by significant figures.
- Scientific notation that keeps exactly the significant figures.
- E-notation input such as 1.20e3 and 4.5 x 10^-3.
- A clear note on the ambiguity of trailing zeros in whole numbers, with a switch.
- Exact decimal arithmetic, no floating-point surprises.
Addition and subtraction rule
Round to the place of the least precise number.
12.11 + 1.013 = 13.123 -> 13.12
150.2 - 3.456 = 146.744 -> 146.7Worked examples
12.11 + 1.013 gives 13.12
Rounded to the hundredths.
150.2 - 3.456 gives 146.7
Rounded to the tenths.
Privacy: how it works
- Everything is calculated by code running in your browser tab. The numbers you enter are not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- Write whole numbers that end in zeros in scientific notation, 1.20 × 10³, so nobody has to guess how many figures you meant.
- Keep extra digits in intermediate steps and round only the final answer.
- For a mixed calculation, apply the multiply rule and the add rule to each step separately and round at the end.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Numbers are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
What is the sig fig rule for adding?
The answer keeps the number of decimal places of the number with the fewest decimal places. It does not depend on how many significant figures each number has.
Why is addition different from multiplication?
Adding combines absolute uncertainties, which depend on the last decimal place, while multiplying combines relative uncertainties, which depend on the number of significant figures.
More Significant Figures Calculator pages
- Significant Figures CalculatorType a measurement to count its significant figures, round it, calculate with it or write it in scientific notation.
- Round to Significant FiguresType a number and how many significant figures to keep.
- Significant Figures MultiplicationEnter two numbers to multiply them and keep the right significant figures.
- Significant Figures DivisionEnter two numbers to divide them and keep the right significant figures.
- Scientific Notation and Sig FigsType a number and get its scientific notation with the right number of digits.
- Significant Figures in Whole NumbersWhole numbers that end in zeros are ambiguous. See how many figures 1200 has and how to say what you mean.