Scientific Notation Calculator

Sig Figs Calculator

Use this sig figs calculator to evaluate expressions, count significant figures, and round results to any precision with a clear step-by-step breakdown.

Evaluate expressions with sig fig trackingRound to 1–25 significant figuresStep-by-step sig fig output

Sig Figs Calculator

Evaluate an expression, round the result to significant figures, and keep the calculation steps ready to copy or download.

Round to significant figures (optional)
Ready

Supports +, -, x, /, ^, parentheses, log, ln, e, pi, and decimals.

Step by Step

    Result Summary

    Answer
    2
    Scientific notation
    2 x 10^0
    E notation
    2e0

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    Sig Figs Calculator

    A sig figs calculator evaluates any numerical expression, counts the significant figures in the result, and rounds it to the precision you specify. Significant figures record how precisely a quantity was measured. In chemistry, physics, and engineering, carrying the wrong number of sig figs can overstate precision or hide measurement uncertainty. This calculator removes the guesswork by showing the sig fig count and a full rounding breakdown in one step.

    What Are Significant Figures?

    Significant figures are the digits in a number that meaningfully communicate measurement precision. The value 4.70 g has three significant figures because the trailing zero signals that the measurement reached the hundredths place. The value 0.0047 has two significant figures because the leading zeros are placeholders, not measured digits. Identifying which digits are significant requires applying consistent rules to non-zero digits, zeros sandwiched between non-zero digits, leading zeros, and trailing zeros both before and after decimal points. Getting these rules right matters because 3.50 m implies a different instrument precision than 3.5 m, even though both equal the same quantity.

    How to Use the Sig Figs Calculator

    Type a number or expression into the input field. The calculator accepts integers, decimals, and compound expressions using addition, subtraction, multiplication, division, exponents, logarithms, and parentheses. Entering an expression such as 1.5 / log(5 + 2) will first evaluate the full expression, then apply sig fig counting and rounding to the result.

    Select how many significant figures you want in the rounded result, from 1 to 25, using the radio buttons or the custom input field. Leave the field empty to count sig figs without rounding. The results panel reports the evaluated value, the rounded answer, the sig fig count, and a numbered breakdown of each calculation step.

    Worked Examples

    Representative examples: 0.00420 has 3 sig figs (4, 2, and the trailing 0); 100.0 has 4 sig figs; the product 2.3 × 4.56 rounds to 10. (2 sig figs because 2.3 limits precision); the sum 12.34 + 0.1 rounds to 12.4 (limited by 0.1's single decimal place); and 1.003 has 4 sig figs including both captive zeros.

    Common Sig Fig Problems

    Frequently solved problems include counting sig figs in values with trailing zeros, rounding products and quotients to the fewest sig figs of any input, applying the decimal-place rule to sums and differences, and determining sig figs in logarithm results where only the mantissa digits count.

    Significant Figures Rules and Reference Tables

    These tables cover the complete rule set for identifying, counting, and rounding significant figures across every category of digit.

    Non-zero digits are always significant

    Every non-zero digit in a number is significant regardless of its position. This rule is the foundation of all sig fig counting and has no exceptions.

    NumberSignificant digitsSig fig countNotes
    73.47, 3, 43All non-zero digits
    0.292, 92Leading 0 is not significant

    Captive zeros are always significant

    A zero sandwiched between two non-zero digits is called a captive or sandwich zero and is always significant because it represents a real measured position.

    NumberAll digitsCaptive zerosSig fig count
    40.074, 0, 0, 7two zeros4
    10031, 0, 0, 3two zeros4

    Leading zeros are never significant

    Leading zeros appear before the first non-zero digit and only mark the position of the decimal. They carry no measurement information and are never significant.

    NumberLeading zerosSignificant digitsSig fig count
    0.0045three zeros4, 52
    0.100one zero1, 0, 03

    Trailing zeros after a decimal point are significant

    When zeros appear to the right of a non-zero digit and a decimal point exists in the number, those trailing zeros are significant because they indicate the precision to which the value was measured.

    NumberTrailing zerosSig fig countInterpretation
    3.50one3Precision to hundredths
    100.00two5Precision to hundredths

    Addition and subtraction: use decimal places

    For addition and subtraction, round the result to match the fewest number of decimal places found in any input value, not the fewest sig figs.

    ExpressionLimiting inputDecimal places keptRounded result
    12.34 + 0.10.1 → 1 decimal place112.4
    8.002 + 1.61.6 → 1 decimal place19.6

    Multiplication and division: use sig fig count

    For multiplication and division, round the result to match the fewest significant figures in any of the input values.

    ExpressionFewest sig figsRounded resultResult sig fig count
    2.3 × 4.562 (from 2.3)10.2
    8.004 / 2.02 (from 2.0)4.02

    Logarithm sig figs: count mantissa digits only

    When a logarithm is calculated, sig figs in the result are counted only in the mantissa—the digits after the decimal point. The characteristic (digits before the decimal) indicates the order of magnitude and does not count as a significant figure.

    ExpressionInput sig figsCorrect resultMantissa sig figs
    log(2.4)20.382
    ln(0.0050)2−5.302

    Process

    Calculation Workflow

    Enter expression
    Evaluate result
    Count sig figs
    Round to precision

    The calculator parses the input, evaluates the expression using standard arithmetic and function rules, determines the number of significant figures in each measured input, and rounds the final result to the specified sig fig count, producing a complete step-by-step breakdown.

    Input Formats

    Supported Formats

    Input styleExample
    Integer1003
    Decimal0.0420
    Expression with log1.5 / log(5 + 2)
    Mixed operations2.30 × 4.56 − 1.2

    Reference

    Common Scientific Constants

    Back to calculator
    Constant nameSymbolNotation valueUnit
    Speed of lightc2.99792458 x 10^8m/s
    Gravitational constantG6.67430 x 10^-11N m^2/kg^2
    Avogadro constantNA6.02214076 x 10^23mol^-1

    Questions

    Calculator FAQ

    What are significant figures?

    Significant figures are the digits in a number that convey meaningful precision about a measurement. All non-zero digits are significant, zeros between non-zero digits are significant, and trailing zeros after a decimal point are significant. Leading zeros are never significant.

    How do I count significant figures in a number?

    Begin at the first non-zero digit and count every digit to the right, including captive zeros and trailing zeros after a decimal point. For example, 0.0407 has three significant figures: 4, 0, and 7. The two leading zeros do not count.

    How many significant figures does 100 have?

    The integer 100 is ambiguous without context. Written as a plain integer, it could have 1, 2, or 3 significant figures. Writing 1.00 × 10² removes the ambiguity and clearly indicates 3 significant figures.

    Are trailing zeros significant?

    Trailing zeros are significant only when they appear to the right of a decimal point, such as 4.50 (three sig figs). In a whole number like 4500, trailing zeros are ambiguous unless a decimal point is written (4500.) or scientific notation is used.

    Are leading zeros significant?

    No. Leading zeros—those to the left of the first non-zero digit—are never significant. In 0.0082, the three zeros at the left are placeholders. Only 8 and 2 are significant, giving two significant figures.

    What is the sig figs rule for addition?

    In addition and subtraction, round the result to match the input with the fewest decimal places. For example, 13.1 + 2.34 = 15.4 because 13.1 has only one decimal place.

    What is the sig figs rule for multiplication?

    In multiplication and division, round the result to match the input with the fewest significant figures. For example, 3.2 × 4.56 = 15 because 3.2 has only two significant figures.

    What is the difference between significant figures and decimal places?

    Decimal places count all digits after the decimal point. Significant figures count only the meaningful digits starting from the first non-zero digit. The value 0.0050 has 4 decimal places but only 2 significant figures.

    How do sig figs apply to exact numbers?

    Exact numbers, such as the 1000 in 'there are 1000 m in 1 km', have unlimited significant figures and never limit the precision of a calculation result.

    What is a captive zero?

    A captive zero sits between two non-zero digits. In 3.07, the zero between 3 and 7 is a captive zero and is significant, giving the number three significant figures.

    How do I round 3.456 to two significant figures?

    Identify the two leftmost significant digits: 3 and 4. The next digit is 5, so round up. The result is 3.5. If the value were 3.449, the result would be 3.4 because the following digit is less than 5.

    How does the sig figs calculator handle logarithm expressions?

    For log or ln expressions, the calculator applies the mantissa rule: only the decimal digits of the logarithm result count as significant figures, matching the sig figs of the input argument.

    Can I use the sig figs calculator for chemistry problems?

    Yes. The calculator supports expressions with arithmetic operators, logarithms, and exponents, making it suitable for chemistry stoichiometry, titration calculations, and equilibrium problems where measurement precision must be tracked.

    Why do significant figures matter in science?

    Significant figures communicate the precision of a measurement. Reporting too many sig figs implies greater precision than your instrument can provide. Reporting too few discards real information. Consistent sig fig rules ensure calculated results accurately reflect original measurement limits.

    What happens when sig fig rules conflict in a multi-step calculation?

    Carry full precision through all intermediate steps and apply sig fig rounding only to the final answer. Rounding at each step introduces cumulative error that can shift the last significant digit of the result.

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