What Are Significant Figures?
Significant figures, also called sig figs, are the digits in a number that convey meaningful information about the precision of a measured value. They include all certain digits in a measurement and the first uncertain digit.
Significant figures are important because measurements are never perfectly exact. Reporting a result with more digits than the measurement supports can give a false impression of precision, while reporting too few digits can remove useful information.
In this guide, you will learn how to identify significant figures, count them in different types of numbers, round values correctly, and apply significant-figure rules to calculations.
Why Do Significant Figures Matter?
Significant figures help communicate the precision of measurements and calculated results.
For example, these two measurements are written differently:
2.5 cm
2.50 cm
Both represent a value of 2.5 cm mathematically, but they communicate different precision. The first has 2 significant figures, while the second has 3.
This distinction matters in subjects and fields that rely on measurements, including chemistry, physics, engineering, laboratory science, and other quantitative disciplines.
The correct number of significant figures depends on the measurement and the rules being used for the calculation.
How to Identify Significant Figures
The main rules for identifying significant figures are based on the position of the digits and zeros within a number.
1. Non-zero digits are always significant
Every non-zero digit from 1 through 9 is significant.
Examples:
7→ 1 significant figure42→ 2 significant figures583→ 3 significant figures27.45→ 4 significant figures
2. Zeros between non-zero digits are significant
A zero between non-zero digits is significant.
Examples:
101→ 3 significant figures1002→ 4 significant figures4.05→ 3 significant figures7.008→ 4 significant figures
These are sometimes called captive zeros because they occur between significant non-zero digits.
3. Leading zeros are not significant
Zeros that appear before the first non-zero digit are not significant. They only locate the decimal point.
Examples:
0.5→ 1 significant figure0.05→ 1 significant figure0.0042→ 2 significant figures0.00670→ 3 significant figures
In 0.00670, the significant digits are 6, 7, and the final 0.
4. Trailing zeros after a decimal point are significant
Zeros written at the end of a decimal number can indicate precision and are therefore significant.
Examples:
2.5→ 2 significant figures2.50→ 3 significant figures2.500→ 4 significant figures0.0700→ 3 significant figures
The written form matters because the additional zeros communicate precision.
5. Trailing zeros in whole numbers can be ambiguous
A whole number such as 1500 does not always make its intended precision clear.
Depending on the context, the trailing zeros may or may not be intended as significant.
Scientific notation provides a clearer way to communicate precision:
1.5 × 10³→ 2 significant figures1.50 × 10³→ 3 significant figures1.500 × 10³→ 4 significant figures
When precision is important, use a notation that clearly communicates the intended number of significant figures.
How to Count Significant Figures
A simple method is to start counting at the first non-zero digit and continue through the number, applying the rules for zeros.
Example 1: 45.67
All four digits are non-zero.
45.67 → 4 significant figures
Example 2: 0.00450
Ignore the leading zeros.
The significant digits are 4, 5, and the final 0.
0.00450 → 3 significant figures
Example 3: 1002
The zeros occur between non-zero digits.
1002 → 4 significant figures
Example 4: 7.080
The zero between 7 and 8 is significant, and the trailing zero after the decimal point is also significant.
7.080 → 4 significant figures
Example 5: 100
This number is ambiguous when written without additional context.
Scientific notation can communicate the intended precision:
1 × 10²→ 1 significant figure1.0 × 10²→ 2 significant figures1.00 × 10²→ 3 significant figures
Significant Figures in Decimal Numbers
Decimal numbers often make significant figures easier to identify because the position of zeros is clearer.
Consider:
0.00450
The zeros before 4 are leading zeros and are not significant. The 4, 5, and final 0 are significant.
Therefore:
0.00450 has 3 significant figures.
Now consider:
4.500
All four digits are significant.
Therefore:
4.500 has 4 significant figures.
Remember that significant figures and decimal places are different. 0.00450 has 3 significant figures but 5 decimal places.
Significant Figures in Scientific Notation
Scientific notation is useful when a number contains many zeros or when its intended precision needs to be made explicit.
Scientific notation has the form:
a × 10ⁿ
The significant figures are contained in the coefficient a. The exponent does not determine the number of significant figures.
Examples:
3.2 × 10⁴→ 2 significant figures3.20 × 10⁴→ 3 significant figures3.200 × 10⁴→ 4 significant figures
Scientific notation can therefore remove ambiguity from numbers such as 1000.
Rounding to Significant Figures
When a number needs to be reported to a specific number of significant figures, follow these steps:
Find the first non-zero digit.
Count the required number of significant digits.
Look at the digit immediately after the last significant digit.
If the next digit requires rounding, increase the last retained digit as appropriate.
Remove the remaining digits or replace them with zeros when necessary.
Example: Round 58.347 to 3 significant figures
The first three significant digits are 5, 8, and 3.
The next digit is 4, so the 3 remains unchanged.
58.347 → 58.3
Example: Round 0.006784 to 3 significant figures
The first three significant digits are 6, 7, and 8.
The next digit is 4, so no increase is required.
0.006784 → 0.00678
Example: Round 9.98 to 2 significant figures
The first two significant digits are 9 and 9. The next digit is 8, so rounding causes the value to increase.
9.98 → 10
Because 10 can be ambiguous, scientific notation can make the intended precision explicit:
1.0 × 10¹
Significant Figures in Addition and Subtraction
Addition and subtraction use a different rule from multiplication and division.
For addition and subtraction, the result is generally rounded to the least precise decimal place among the values being combined.
Example
12.11 + 0.3 = 12.41
12.11 is precise to the hundredths place.
0.3 is precise only to the tenths place.
Therefore, the result should be reported to the tenths place:
12.4
The rule is:
Addition and subtraction → round to the least precise decimal place.
Significant Figures in Multiplication and Division
For multiplication and division, the result is generally reported with the same number of significant figures as the input value with the fewest significant figures.
Example
4.5 × 2.13 = 9.585
4.5 has 2 significant figures.
2.13 has 3 significant figures.
Therefore, the result should be reported with 2 significant figures:
9.6
The rule is:
Multiplication and division → round to the fewest significant figures.
Do Not Round Intermediate Results Too Early
In a multi-step calculation, rounding every intermediate result can introduce additional rounding error.
When appropriate, retain extra digits during intermediate steps and round the final result according to the required precision.
Your instructor, laboratory procedure, textbook, or professional standard may specify a particular method for handling intermediate values, so follow those instructions when they apply.
Exact Numbers vs Measured Numbers
Not every number in a calculation comes from a measurement.
A counted quantity, such as 12 students, is an exact count within that context. It does not have measurement uncertainty in the same way as a measured value.
Defined quantities can also be treated as exact under the relevant convention.
For example, if a calculation uses an exact count or an exact defined relationship, it should not automatically be treated as though it had the same measurement limitations as an experimentally measured quantity.
The treatment of exact values can depend on the context and the conventions being followed.
Significant Figures vs Decimal Places
Significant figures and decimal places describe different aspects of a number.
Significant figures count meaningful digits beginning with the first non-zero digit.
Decimal places count the number of digits after the decimal point.
For example:
0.00450
has:
3 significant figures
5 decimal places
Another example:
12.30
has:
4 significant figures
2 decimal places
A number can therefore have many decimal places but relatively few significant figures.
Worked Examples
Example 1: 0.00340
Leading zeros are not significant.
The significant digits are 3, 4, and the final 0.
Answer: 3 significant figures
Example 2: 4050
The zero between 4 and 5 is significant.
The final zero is potentially ambiguous when the number is written without a decimal point or scientific notation.
Scientific notation can clarify the intended precision.
Example 3: 7.080
The zero between non-zero digits is significant, and the final zero after the decimal point is significant.
Answer: 4 significant figures
Example 4: 3.45 × 2.1
3.45 has 3 significant figures.
2.1 has 2 significant figures.
The result should therefore be reported with 2 significant figures.
3.45 × 2.1 = 7.245 → 7.2
Example 5: 18.2 + 1.35
The calculation gives:
18.2 + 1.35 = 19.55
The least precise value is 18.2, which is precise to the tenths place.
Therefore:
19.55 → 19.6
Common Significant-Figure Mistakes
Mistake 1: Counting leading zeros
0.0042 does not have 4 significant figures.
It has:
2 significant figures
Mistake 2: Assuming every zero is significant
The position of a zero matters. A leading zero is different from a zero between non-zero digits or a trailing zero in a decimal number.
Mistake 3: Confusing significant figures with decimal places
The number of significant figures and decimal places can be completely different.
Mistake 4: Using the multiplication rule for addition
Addition and subtraction are based on decimal-place precision, not simply the number of significant figures.
Mistake 5: Treating 100 as automatically having three significant figures
A number such as 100 can be ambiguous. Scientific notation can communicate the intended precision more clearly.
Mistake 6: Rounding too early
Premature rounding during a multi-step calculation can affect the final result.
How Our Significant Figures Calculator Can Help
If you need to check a value quickly, how our Significant Figures Calculator works.
The calculator can help you determine the number of significant figures in a number and perform supported rounding calculations.
For best results, enter the value exactly as it appears in your problem or measurement. Do not remove zeros before entering the number because their position may affect its significant figures.
If you are unsure why a result was produced, use the rules and worked examples on this page to verify the calculation.
Frequently Asked Questions
What are significant figures?
Significant figures are the digits in a measured or calculated value that communicate meaningful precision.
How many significant figures does 0.00450 have?
0.00450 has 3 significant figures: 4, 5, and the final 0.
How many significant figures does 100 have?
100 can be ambiguous when written without additional context. Scientific notation can be used to show the intended precision, such as 1 × 10², 1.0 × 10², or 1.00 × 10².
Are leading zeros significant?
No. Leading zeros only locate the decimal point and do not count as significant figures.
Are zeros between non-zero digits significant?
Yes. A zero between non-zero digits is significant.
Are trailing zeros significant?
Trailing zeros after a decimal point are significant when they are written as part of the measured value. Trailing zeros in whole numbers can be ambiguous without additional context.
What is the rule for addition and subtraction?
Round the result to the least precise decimal place among the values being added or subtracted.
What is the rule for multiplication and division?
Report the result using the number of significant figures in the input value with the fewest significant figures.
Are significant figures the same as decimal places?
No. Significant figures count meaningful digits, while decimal places count digits after the decimal point.
Summary
Significant figures communicate the precision of measured and calculated values.
The most important rules are:
Non-zero digits are significant.
Zeros between non-zero digits are significant.
Leading zeros are not significant.
Trailing zeros after a decimal point are significant.
Trailing zeros in whole numbers can be ambiguous.
Scientific notation can clarify intended precision.
Addition and subtraction use decimal-place precision.
Multiplication and division use significant-figure precision.
Exact numbers may be treated differently from measured values.
Avoid unnecessary rounding during intermediate calculations.
Understanding significant figures is essential whenever measurements and calculated results need to be reported with appropriate precision.
Use the [Significant Figures Calculator] to check your values, and use the explanations and examples in this guide to understand how the result is determined.
References
For additional information about measurement, significant digits, and numerical precision, consult authoritative scientific and educational references appropriate to your field or course requirements.