Sig Fig (Significant Figures) Calculator (2024)

The significant figures calculator undertakes calculations with significant figures and works out how many significant figures (sig figs), i.e., digits, a number holds.

Simply input a number or mathematical expression, then click the "Calculate" button for the answer.

Operators and functions that are supported:

  • Arithmetic operators: addition ( + ), subtraction ( - ), division ( / or ÷ ), multiplication ( * or × ) and exponent ( ^ )
  • Group symbols: ( )
  • Functions: log n, ln n
  • Constants: pi, e

Exact quantities

  • In calculating with sig figs one sometimes encounters quantities that are exact as opposed to having limited accuracy. You can enter an exact quantity by appending an # to end of the number; e.g. 3.2#. For instance, if you want to convert 3.00045 g sulfur to moles using sulfur's molecular weight of 32.06 g/mol you would use the following calculation:
  • 3.00045 / 32.06# = 0.0935886 mol sulfur
  • as opposed to the calculation:
  • 3.00045 / 32.06 = 0.09359 mol sulfur
  • where 32.06 is taken to only have 4 significant figures and accuracy is thereby lost in this calculation.

Rules:

This calculator applies a set of rules to determine significant figures. These are outlined below:

  • Addition / subtraction rounded to the lowest number of decimal places.
  • Multiplication / division rounded to the lowest number of significant figures.
  • Logarithms rounded so that a number of significant figures in the input match the number of decimals in the result.
  • Exponentiation rounded to the certainty in the base only.
  • To enumerate trailing zeros, it places a decimal point after the number (e.g., 100000.) or express it in scientific terms (e.g., 1.00000 × 10^5 or 1.00000e+5).
  • Rounds on the last step, following parentheses, when appropriate.

Describing Significant Figures

When we report values that are derived from a measurement or that were calculated by employing measured values, we need a method by which we can determine the measurement's level of certainty. We can do this by employing significant figures.

Significant figures represent the digits within a value that we have a certain amount of confidence that we know. As the quantity of significant figures rises, the measurement becomes more certain. As the measurement becomes more precise, the number of significant figures increases.

Rules for significant figures

1) Every digit that is not zero is significant.

  • For example:
  • 2.437 includes four significant figures
  • 327 includes three significant figures

2) When zeros are between digits that are not zeros, they are significant.

  • For example:
  • 700021 includes six significant figures
  • 3049 includes four significant figures

3) When a zero is to the left of the first digit that is not a zero, it is not significant.

  • For example:
  • 0.003333 includes four significant figures
  • 0.00098 includes two significant figures

4) Trailing zeros (zeros which come after the final non-zero digit) are significant if the number contains a decimal point.

  • For example:
  • 8.000 includes four significant figures
  • 800. includes three significant figures
  • 0.080 includes two significant figures

5) If the number does not have a decimal point, trailing zeros are not significant.

  • For example:
  • 500 or 5 × 10^2 only includes one significant figure
  • 51000 includes two significant figures

6) In scientific notation, all digits before the multiplication sign are significant.

  • For example:
  • 1.603 × 10^-4 includes four significant figures

7) The number of significant digits in exact numbers is infinite. This is also true for defined numbers.

  • For example:
  • 1 meter = 1.0 meters = 1.000 meters = 1.00000000 meters etc.

Examples of Significant Figures

Number# of Sig FigsSignificant Figures
10011
100.041, 0, 0, 0
0.0111
0.0515
7127, 1
12500031, 2, 5
0.1050051, 0, 5, 0, 0
0.002522, 5
15000.1571, 5, 0, 0, 0, 1, 5
0.075037, 5, 0
0.1012051, 0, 1, 2, 0
1500.41, 5, 0, 0
7.128 × 10-347, 1, 2, 8

Significant Figures Quiz

Determine the number of significant figures in each of the following measurements.

You Scored % - /

Measurement: 5.72 lbs

Significant Figures?

Measurement: 500.243 mg

Significant Figures?

Measurement: 0.00068 cm

Significant Figures?

Measurement: 14.0 acres

Significant Figures?

Measurement: 500 tons

Significant Figures?

Measurement: 1.402 × 1018 atoms

Significant Figures?

Significant figures in operations:

Addition and subtraction

With addition and subtraction, you should round your final result so its precision (number of decimal places!) matches the precision of the least precise number, no matter how many significant figures any particular term possesses. For example:

87.221 + 1.2 = 88.421 but you should round this value down to 88.4 (so that it matches the precision of the least precise number in the sum, 1.2)

Multiplication, division, and roots

In multiplication, division or when taking roots, your results should be rounded so that the final result has the same number of significant figures as the number with the least number of significant figures. For example:

3.14 × 2.2048 = 6.923072 but you should round this value down to 6.92 (the measurement with the least significant figures is 3.14, which has 3 significant figures, rounding to 3 sig figs gives 6.92)

Logarithms

If you are calculating the logarithm of a number, you should make sure that the mantissa (the figure to the right of the decimal point in the answer) contains an identical number of significant figures as the number of significant figures of the number of which the logarithm is being calculated. For example:

log (2×10^5) = 5.301029995663981 - you should round this figure to 5.3

Multiple Mathematical Operations

Should a calculation require a number of mathematical operations to be combined, do it with more figures than the number that will be significant to get your value. Then review the calculation and, by applying the rules above, calculate the number of significant figures needed in the final result.

You may also be interested in our Scientific Notation Calculator

Sig Fig (Significant Figures) Calculator (2024)

FAQs

How many sig figs should my answer be? ›

When adding/subtracting, the answer should have the same number of decimal places as the limiting term. The limiting term is the number with the least decimal places. When multiplying/dividing, the answer should have the same number of significant figures as the limiting term.

How to calculate answers to the appropriate number of significant figures? ›

There are three rules on determining how many significant figures are in a number:
  1. Non-zero digits are always significant.
  2. Any zeros between two significant digits are significant.
  3. A final zero or trailing zeros in the decimal portion ONLY are 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 0.9968 rounded to 2 significant figures? ›

The value given was 0.9968 which is to change into to 2 significant figures, if we count from the right hand, it will remain 0.99 which can be rounded up 1.00 because 9 is more that 5.

How to know how many sig figs to use when measuring? ›

Determining the Number of Significant Figures

The number of significant figures in a measurement, such as 2.531, is equal to the number of digits that are known with some degree of confidence (2, 5, and 3) plus the last digit (1), which is an estimate or approximation.

How many significant figures should each answer be rounded? ›

Observed values should be rounded off to the number of digits that most accurately conveys the uncertainty in the measurement. Usually, this means rounding off to the number of significant digits in in the quantity; that is, the number of digits (counting from the left) that are known exactly, plus one more.

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 many sig figs are in 11 soccer players? ›

Final answer:

'11 soccer players' and '507 thumbtacks' aren't considered in terms of significant figures because they are counts, not measurements. '0.070020 meter' has 5 significant figures, '10,800 meters' has 3, '0.010 square meter' has 2, and '5.00 cubic meters' has 3.

How to know how many sig figs to use when multiplying? ›

The rule in multiplication and division is that the final answer should have the same number of significant figures as there are in the number with the fewest significant figures.

Does 0.202 have 3 significant figures? ›

Zeroes at the right end after the decimal point are significant but if the zeroes are used for spacing for the decimal place, it is not considered significant (examples are the zeroes before and after the decimal point). From the given choices, (c) 0.202 g is expressed in 3 significant figures.

Does 0.510 have 3 significant figures? ›

Answer and Explanation:

The numbers are 0,5,1 and 0. The zero before the decimal point is not significant. But the non zero digits and the zero after the nonzero digits are significant in nature. Hence the number of significant digits are three.

Does 0.200 have 3 significant figures? ›

0.200contains 3 while 200 contains only one significant figure because zero at the end or right of a number are significant provided they are on the right side of the decimal point.

How do you round 78.56 to two significant figures? ›

Round 78.56 to two significant figures. The first significant figure is 7 7 7 and the second is 8 8 8. The next number to the right is 5 5 5, so we round up. Adding one to the 8 8 8 gives us 9 9 9 and therefore we have 79 79 79.

What is 6.998 rounded to 2 significant figures? ›

6 Ali says that 6.998 rounded to 2 significant figures is 7.

What is $9.99 rounded to 2 sig figs? ›

9.99 rounded to 2 sig. 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.

How do you write an answer in sig figs? ›

Every non-zero digit is significant. Zeros in between non-zero digits are significant. Zeros at the end of the answer when no decimal point is specified are not significant. Zeros at the end of the answer when a decimal point is specified are significant.

How do you give your answer to 3 significant figures? ›

We round a number to three significant figures in the same way that we would round to three decimal places. We count from the first non-zero digit for three digits. We then round the last digit. We fill in any remaining places to the right of the decimal point with zeros.

How many significant figures does 10.0 have? ›

There are 3 significant figures.

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