Significant Figures Calculator & Counter (Sig Fig Calculator) (2024)

Use this tool in significant figures calculator mode to perform algebraic operations with numbers (adding, subtracting, multiplying and dividing) with the appropriate significant digit rounding. In significant figures counter mode it will count the number of significant digits in a number. Use the calculator in rounding mode to round a number to a given number of significant figures.

Quick navigation:

  1. What are significant figures?
  2. Significant figures rules
  • Significant digits examples
  • Counting significant figures
  • Rounding significant figures
  • Algebraic operations with rounding
    • Significant figures addition rule
    • Significant figures multiplication rule

    What are significant figures?

    Significant figures (a.k.a. significant digits or precision) of a number written in positional notation are all digits that carry meaningful contributions to its measurement resolution. Of the significant figures in a number the one in the position with the highest exponent value (the left-most) is the most significant, while the one in the position with the lowest exponent value (the right-most) is the least significant.

    Significant digits are important in different areas where measurements apply and are usually used to express the precision of measurements. Numbers can be rounded to a given number of significant figures, for example when the measurement device cannot produce accurate results to a given resolution. Counting how many digits are significant is done by following several simple rules. Our sig fig calculator can help with all of these operations.

    Significant figures rules

    The rules for which digits in a positional notation are significant are simple. All figures are significant except the following:

    1. Leading zeroes, e.g. "00123" has three significant figures: 1, 2, and 3. 0.0012 has just two significant figures: 1 and 2.
    2. Trailing zeros when they are merely placeholders to indicate the scale of the number. This means that zeroes to the right of the decimal point and zeroes between significant figures are themselves significant.
    3. Digits beyond the required or supported precision. E.g. figures introduced by division or multiplication or measurements reported to a greater precision than the measurement equipment supports.

    Note that the above rules mean that all non-zero digits (1-9) are significant, regardless of their position. Use our significant digits calculator in "counter" mode to count and examine the significant figures in any number.

    See below for the rules for rounding when performing arithmetic operations with numbers with a given precision.

    Significant digits examples

    The following table contains examples of applying the significant digits rules above in a variety of cases that cover everything you should see in practice.

    Examples with a different number of significant figures
    Original numberSignificant figuresCount of significant figuresRules applied
    0.00551#1
    0383,82#1
    4704,72#2
    470.4,7,03#2
    470.04,7,0,04#2
    0205.602,0,5,6,05#1,#2
    1001.051,0,0,1,0,56#2
    121001,2,13#2
    121.0901,2,1,0,9,06#2

    Of the above examples, the most tricky to understand are:

    • 0205.60: here the leading zero is dropped via rule #1, the zero between 2 and 5 is preserved as it is between two significant digits and the trailing zero is preserved as it is to the right of the decimal point (both following rule #2)
    • 470.0: here the trailing zero is significant as it is to the right of the decimal point, while the other zero is also significant since it sits between two significant figures: the seven to the left and the zero beyond the decimal point
    • 1001.05: the first two zeroes are between significant digits greater than zero, the third zero is also significant since it is both to the right of the decimal point and is between two significant digits

    Counting significant figures

    Counting the number of significant digits is done simply by identifying them using the rules, and then performing a simple count. For examples, see the table above. To count significant figures using this calculator, simply put the tool in "counter" mode and enter the number you want to count the significant digits of.


    Rounding significant figures

    Numbers are often rounded to a specified number of significant figures for practicality, e.g. to present in a news broadcast or to put down in a table neatly. Rounding a number to n significant figures happens in a similar way to rounding to n decimal places, with an important difference. We start by counting from the first non-zero digit for n significant digits and then round the last digit. However, we do not fill in the remaining places to the right of the decimal point with zeroes.

    In more detail, the process of rounding to n significant digits is as follows:

    1. Identify the first n significant figures in the number, left to right.
    2. If the digit immediately to the right of the n-th digit is greater than or equal to 5, and to its right there are non-zero digits, add 1 to the n-th digit.
    3. If the digit immediately to the right of the n-th digit is 5, and to its right there are only zeroes or nothing, there is a tie. To break the tie using the half away from zero rule, add 1 to the n-th digit. If using the half to even method, preferred in scientific settings as it does not produce upwardly skewed numbers, round down to the nearest even number.
    4. Replace non-significant figures in front of the decimal point by zeroes.
    5. Drop all the digits after the decimal point to the right of the n significant figures.

    An example of the rounding rule application, consider the number 1.55 and rounding it to 2 significant figures. Using both methods would result in rounding it to 1.6 since this is also the nearest even number. However, if the original number was 1.45, rounded to two significant figures it would become 1.5 under the half away from zero method, but 1.4 under the half to even method.

    Examples of rounding to n significant figures

    Rounding with a given precision based on decimal places differs from rounding to the same precision of significant figures. Examples of rounding of the number 12.345 are presented in the table below.

    Rounding 12.345 to different levels of precision
    Rounding precision (n)To n significant figuresTo n decimal places
    712.3450012.3450000
    612.345012.345000
    512.34512.34500
    412.35*12.3450
    312.312.345
    21212.35*
    11012.3
    0N/A12

    * using the half to even rule it would round to 12.34.

    In another example, take the number 0.012345. The rounding calculations are presented in the table below.

    Rounding 0.012345 to different levels of precision
    Rounding precision (n)To n significant figuresTo n decimal places
    70.012345000.0123450
    60.01234500.012345
    50.0123450.01235*
    40.01235*0.0123
    30.01230.012
    20.0120.01
    10.010.0
    0N/A0

    * using the half to even rule it would round to 0.01234.

    You can check the accuracy of by using our rounding significant figures calculator.

    Algebraic operations with rounding

    Using our tool in significant figures calculator mode you can perform addition, subtraction, multiplication and division of numbers expressed in a scientific notation to a given degree of precision. Our tool will automatically apply the appropriate rounding rule depending on the selected mathematical operation, as explained below.

    Significant figures addition rule

    The rule for adding significant figures is to round the result to the least accurate place. The sum or difference is to be rounded to the same number of decimal places as that of the measurement with the fewest decimal places which reflects the fact that the answer is just as precise as the least-precise measurement used to compute it. For example, 2.24 + 4.1 = 5.34 which has to be rounded to one place after the decimal dot, since 4.1 is only precise to that level, giving a result of 5.3. If we were adding 2.24 and 4.10 though, the result would be 5.34.

    Our significant figures calculator uses this rule automatically. You can choose if the rounding is done using the half away from zero rule or by the half to even rule. The rule for adding is also used for subtraction of numbers with a given number of significant digits.

    Significant figures multiplication rule

    Multiplication rounding and division rounding is performed based on the number of significant figures in the measurement with the lowest count of significant digits. For example, multiplying 20.0 by 10 will result in 200. Since only a single digit ("1") is significant in the second number rounding to the first significant digit gives us 200 of which only the "2" is significant. In another example, let us say we multiply 2.5 by 10.05 and get 25.125. Since 2.5 has only two significant digits, we must round the result to two significant digits as well, giving us an answer of 25. This rounding rule is applied automatically in our tool.

    The least number of significant digits rule is used both for multiplication and for division of numbers in our calculator.

    Significant Figures Calculator & Counter (Sig Fig Calculator) (2024)

    FAQs

    How do I know how many sig figs to put in my answer? ›

    Determining significant figures:
    1. Any nonzero digit is significant.
    2. Zeros between nonzero digits are significant.
    3. The final zeros to the right of the decimal point are significant.
    4. Zeros before the first nonzero digit are not significant.

    What is 0.9999 to 3 significant figures? ›

    Answer and Explanation:

    This means that 0.9999 rounded to three decimal places is 1.000.

    What is 0.9976 to 2 significant figures? ›

    Final answer:

    To round 0.9976 to 2 significant figures, you would get 1.0 x 10^0.

    How many sig figs should my final answer be? ›

    The number of sig figs in the final calculated value will be the same as that of the quantity with the fewest number of sig figs used in the calculation. In practice, find the quantity with the fewest number of sig figs.

    How many sig figs does 3.00 have? ›

    For example, 3.0 (2 significant figures ) 12.60 (4 significant figures) = 37.8000 which should be rounded off to 38 (2 significant figures). (1) If the digit to be dropped is greater than 5, the last retained digit is increased by one. For example, 12.6 is rounded to 13.

    How many sig figs does 10.0 have? ›

    There are 3 significant figures.

    How is 2500 correct to 2 significant figures? ›

    By convention, it is assumed that trailing zeros without a decimal point are not significant. For example, 250.0 has four significant figures, but 2500 only has two definitive significant figures. In these cases, it is best to write the number in scientific notation to avoid ambiguity.

    What is 9.99 to 1 significant figure? ›

    fig. is 10. This may seem strange, because the number 10 only has 1 significant figure, but 9.99 rounded to 2 significant figures must be 10, because rounding it to 1 would be much too small.

    Is 0.7 two significant figures? ›

    How do I decide how many digits to round off to? Well, by the addition rule, the result of the subtraction must be rounded to 1 decimal digit, because 0.7 has only 1 decimal digit. This will leave a 1 significant figure number.

    What are the 7 rules of significant figures? ›

    Significant Figures
    • All non-zero numbers ARE significant. ...
    • Zeros between two non-zero digits ARE significant. ...
    • Leading zeros are NOT significant. ...
    • Trailing zeros to the right of the decimal ARE significant. ...
    • Trailing zeros in a whole number with the decimal shown ARE significant.

    Do leading zeros count as sig figs? ›

    Zeros that appear in front of all of the nonzero digits are called leading zeros. Leading zeros are never significant. 0.008 has one significant figure. 0.000416 has three significant figures.

    How many sig figs is 900? ›

    Leading zeroes are never significant. Trailing zeroes are only significant if they are after a decimal, or are followed by a decimal. Example: 0.900 has 3 sig figs. 900 only has 1 sig fig.

    How do you calculate the number of significant figures? ›

    All zeros that occur between any two non zero digits are significant. For example, 108.0097 contains seven significant digits. All zeros that are on the right of a decimal point and also to the left of a non-zero digit is never significant. For example, 0.00798 contained three significant digits.

    What are the 5 rules for significant figures? ›

    Rules for significant figures
    • All nonzero digits are significant. ...
    • All zeros that are found between nonzero digits are significant. ...
    • Leading zeros (to the left of the first nonzero digit) are not significant. ...
    • Trailing zeros for a whole number that ends with a decimal point are significant.
    May 27, 2024

    How do you determine how many sig figs an answer should be rounded to in a multiplication or division problem? ›

    For multiplication and division problems, the answer should be rounded to the same number of significant figures as the measurement with the least number of significant figures.

    How do you count sig figs examples? ›

    • All non-zero digits are always significant.
    • Interior zeros (zeros between nonzero numbers) are significant.
    • 0.02503 (4 sig. figs.)
    • 402 (3 sig. figs.)
    • 00674 (6 sig. figs.)
    • Leading zeros (zeros at the beginning of a number) are NOT.
    • significant.

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