MathGPT ScientificFree scientific workspace
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Count and round to significant figures
Use the free significant figures calculator to work through the number relationship, preserve exact values, and check the result with estimation. Calculate with natural scientific notation, reusable history, angle modes, memory, probability functions, and familiar calculator layouts.
Arithmetic
Significant Figures Calculator explained
The short version
- Significant figures say how many digits in a measurement were really measured, not guessed.
- Start counting at the first digit that is not zero, and never count the zeros in front of it.
- Multiplying keeps the fewest significant figures; adding keeps the fewest decimal places.
The formula this page uses
Count from the first non-zero digit. × and ÷ → keep the fewest significant figures. + and − → keep the fewest decimal places.
What each part means
SymbolWhat it means
significant figure — A digit that carries informationThe digits somebody actually read off an instrument.
leading zero — A zero in front of the first real digitAs in 0.0038. It only marks the place and never counts.
trailing zero — A zero on the endIt counts if there is a decimal point in the number, as in 45.60.
captive zero — A zero between two digitsAs the two zeros in 100.05. These always count.
Show your work: a full example
- Work out 4.56 × 1.4 to the right precision4.56 × 1.4
- Count the first number's significant figures4, 5 and 6, so 3 significant figures
- Count the second one's1 and 4, so 2 significant figures
- Multiply exactly first4.56 × 1.4 = 6.384
- Keep the fewest, which is 2round 6.384 to 2 significant figures
- Write the answer6.4
A second, different case
- A different case: addition uses a different rule12.11 + 8.3
- Add exactly first12.11 + 8.3 = 20.41
- Count decimal places, not significant figures12.11 has 2 decimal places, 8.3 has 1
- Keep the fewest, which is 120.41 rounds to 20.4
- Notice what would go wrongtheir significant-figure counts are 4 and 2, and using 2 here would give 20, which is far too rough
- Now count a number with leading zeros0.004560 has significant digits 4, 5, 6 and 0
- Read the count4 significant figures, because the three zeros in front only mark the place
Copy-ready example
4.56 × 1.4
Work out 4.56 × 1.4 to the right precision
Questions about the Significant Figures Calculator
Why do adding and multiplying use different rules?
Because the errors behave differently. When you add 12.11 to 8.3, the second number is only trustworthy to a tenth, so the sum cannot be trusted past a tenth either. When you multiply, the error grows in proportion, so it is the count of trustworthy digits that carries through instead.
Do counted numbers limit the precision too?
No. If you weigh 3 identical bolts at 4.56 g each, the 3 is exact because you counted it, not measured it. So 3 × 4.56 = 13.68 g keeps 3 significant figures from the measurement, and the counted 3 imposes no limit at all.
How do I write 1200 to exactly three significant figures?
Use scientific notation: 1.20 × 10³. Written as 1200 nobody can tell whether the zeros were measured, and adding a decimal point to make 1200. claims all four. Scientific notation is the only form that says precisely what you mean.
Should I round after every step of a long calculation?
No, keep the extra digits until the very end and round once. Rounding at each stage lets small errors pile up, and a three-step calculation can easily end up wrong in the last digit that you were meant to report.
How to use a scientific calculator accurately
The calculator executes the expression entered; mathematical judgment still determines the correct expression, mode, and interpretation.
Set the angle mode
Use degrees for degree-labelled angles and radians for calculus or unit-circle work unless the problem states otherwise. A correct key sequence in the wrong mode produces a wrong value.
Group the expression
Use parentheses around numerators, denominators, exponents, and negative substitutions. Read the full display before evaluating.
Keep precision until the end
Reuse the stored answer instead of a rounded display value during multi-step work, then round once to the requested precision and units.
Estimate and verify
Predict sign and scale, use identities or inverse operations, and compare a second entry when the result matters.
About the calculator layouts
The MathGPT, TI-84 Plus-style, HP Prime-style, Casio fx-CG50-style, and Casio fx-9860GIII-style key arrangements share one independent calculation engine. They provide familiar practice layouts and do not emulate proprietary firmware or imply affiliation with those manufacturers.
Learn the mathematics
Understand arithmetic behind this calculator
A calculator confirms an answer. Working the method yourself is what makes the next problem faster.
GuidesLearn arithmeticConcepts, worked methods, and checks.
PracticePractice arithmetic questionsAnswer review after every attempt.
ReferenceArithmetic formulasConditions and examples for each formula.