Sig Fig (Significant Figures) Calculator | Good Calculators

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

Significant Figures Quiz

Determine the number of significant figures in each of the following measurements.You Scored % - /Measurement: 5.72 lbsSignificant Figures? Simply count the number of digits in this measurement. The 5 in the ones place, the 7 in the tenths place, and the 2 in the hundredth place.Measurement: 500.243 mgSignificant Figures? Since we know the measurement down to the thousandths place, we must also know for certain the tenths and ones place. Therefore these zeros must carry significance.Measurement: 0.00068 cmSignificant Figures? The leading zeros in this decimal measurement are only place holders and thereby impart no significance.Measurement: 14.0 acresSignificant Figures? Remember, trailing zeros in the decimals place still contribute meaning as they aren't needed as place holders and thereby count in sig figs.Measurement: 500 tonsSignificant Figures? As before, count the number of digits, but now we know not to include trailing zeros.Measurement: 1.402 × 1018 atomsSignificant Figures? Remember that all of the digits before the multiplication sign - and only these digits - contribute significance.Check Answers

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.

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