About Significant Figures Multiplication
This calculator multiplies measured numbers and rounds the product to the number of significant figures of the least precise factor. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The page opens on 4.56 × 1.4. The exact product is 6.384. The first factor has three significant figures and the second has two, so the answer has two: 6.4.
Trailing zeros after a decimal point count: 0.0230 × 12.50 has three and four significant figures, so the answer has three: 0.288. The calculator shows each count in the steps.
How to use Significant Figures Multiplication
- 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.
Multiplication rule
Count the significant figures of each factor and use the smaller number.
4.56 (3) × 1.4 (2) = 6.384 -> 6.4 (2)Worked examples
4.56 × 1.4 gives 6.4
Two significant figures.
0.0230 × 12.50 gives 0.288
Three significant figures, from 0.0230.
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.
How many significant figures should a product have?
As many as the factor with the fewest significant figures.
Do exact numbers limit the answer?
No. A counted number like 3 apples, or a defined factor like 100 cm per metre, is exact and does not reduce the number of 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 AdditionEnter two numbers to add or subtract them and keep the right precision.
- 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.