Significant Figures Calculator

Count significant figures, round numbers to any number of significant digits, and calculate with the correct sig fig rules for addition, subtraction, multiplication, and division.

Operation

Enter a Number

Integers, decimals, negatives, and scientific notation (1.20e3 or 1.20 × 10³) are supported. The written form is preserved for analysis.

Round to (significant figures)

First Number

Operation

Second Number

Quick examples

Significant Figures

Significant digits

4, 5, 0

Digit analysis

sig = significant 0 = leading zero 0 = ambiguous trailing

Why?

Minimum clear count (non-zero + interior zeros)

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Standard notation

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Scientific notation

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Rounded to

3 significant figures

Explanation

Expression

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Exact calculation

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Final answer

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Precision rule

How to Use the Significant Figures Calculator

Step-by-step method to count, round, and calculate with significant figures correctly.

1. Choose your operation: Select whether you want to count significant figures, round a number, or perform arithmetic (addition, subtraction, multiplication, division).
2. Enter your numbers: Input the number(s) you want to analyze. Scientific notation (e.g., 1.20e3) and trailing decimal points (e.g., 100.) are fully supported.
3. Select rounding target (if applicable): If using Round mode, choose how many significant figures you want to round to.
4. Review the analysis: See the visual digit breakdown, the exact rule applied, and the final correctly rounded or calculated result.

What Are Significant Figures?

Significant figures (also called significant digits) are the digits in a measured or calculated value that communicate its meaningful precision. They tell you how precise a measurement is.

123.4 → 4 significant figures
0.00450 → 3 significant figures
1.200 → 4 significant figures

Significant Figures Rules

Non-zero digits: Always significant (e.g., 123 = 3)
Zeros between non-zero digits: Significant (e.g., 1002 = 4)
Leading zeros: Not significant (e.g., 0.0045 = 2)
Trailing decimal zeros: Significant (e.g., 1.200 = 4)
Whole-number trailing zeros: Can be ambiguous (e.g., 1200)

How to Count Significant Figures

All non-zero digits are significant.
Zeros between non-zero digits are significant.
Leading zeros (before the first non-zero digit) are never significant.
Trailing zeros after a decimal point are significant.
Trailing zeros in a whole number without a decimal point are ambiguous — use scientific notation to clarify.

How to Round to Significant Figures

Start at the first non-zero digit.
Count the requested number of significant digits.
Look at the next digit.
If the next digit is less than 5, leave the last significant digit unchanged (round down).
If the next digit is 5 or greater, increase the last significant digit by 1 (round half up).
Preserve trailing zeros when they are needed to show the requested precision (e.g., 1.2 rounded to 4 sig figs becomes 1.200).

Example: 12,345 rounded to 3 significant figures → 12,300 (or 1.23 × 10⁴).

Significant Figures in Addition and Subtraction

The answer is rounded based on the smallest number of decimal places, not the smallest number of significant figures.

Example: 12.11 + 18.0 + 1.013

12.11 has 2 decimal places
18.0 has 1 decimal place
1.013 has 3 decimal places

Exact sum = 31.123 → final answer 31.1 (limited by the 1 decimal place of 18.0).

Significant Figures in Multiplication and Division

The final answer has the same number of significant figures as the input with the fewest significant figures.

Example: 4.56 × 1.4

4.56 has 3 significant figures
1.4 has 2 significant figures

Exact product = 6.384 → final answer 6.4.

Significant Figures in Scientific Notation

Only the coefficient determines the number of significant figures. The exponent does not affect the count.

1.2 × 10³ → 2 significant figures
1.20 × 10³ → 3 significant figures
1.200 × 10³ → 4 significant figures

Trailing Zeros and Ambiguous Numbers

100 → ambiguous without additional context
100. → 3 significant figures (decimal point makes the zeros significant)
100.0 → 4 significant figures
1.00 × 10² → 3 significant figures

Scientific notation is the clearest way to communicate intended precision when trailing zeros appear in whole numbers.

Common Significant Figures Mistakes

Counting leading zeros: 0.0045 has 2 significant figures, not 4.
Confusing decimal places with significant figures: 12.34 rounded to 3 significant figures is 12.3, not 12.340.
Ignoring written trailing zeros: 1.20 and 1.2 do not have the same precision.
Using the wrong arithmetic rule: Addition/subtraction uses decimal places; multiplication/division uses significant figures.
Rounding intermediate calculations too early: Keep full precision during intermediate steps and round only the final answer.

Frequently Asked Questions

Q: What are significant figures?

Significant figures are the digits in a number that carry meaningful information about its precision. They include all non-zero digits, zeros between non-zero digits, and trailing zeros after a decimal point.

Q: How many significant figures are in 0.00450?

3 significant figures. Leading zeros are not significant; the digits 4, 5, and the trailing zero after the decimal are significant.

Q: How many significant figures are in 100?

Ambiguous. Without a decimal point the trailing zeros may or may not be significant. Use scientific notation (1 × 10², 1.0 × 10², or 1.00 × 10²) to make the intended precision clear.

Q: How many significant figures are in 100.0?

4 significant figures. The decimal point and trailing zero make all four digits significant.

Q: How do you round to 3 significant figures?

Identify the first three significant digits, look at the next digit, and round using the half-up rule (5 or greater rounds up). Preserve trailing zeros when needed to show precision (e.g. 1.2 → 1.20 when rounding to 3 sig figs).

Q: What is the difference between decimal places and significant figures?

Decimal places count digits after the decimal point. Significant figures count all meaningful digits from the first non-zero digit. Addition/subtraction is limited by decimal places; multiplication/division is limited by significant figures.

Q: How do significant figures work in addition and subtraction?

The result is rounded to the least number of decimal places present in any of the input numbers.

Q: How do significant figures work in multiplication and division?

The result is rounded to the same number of significant figures as the input that has the fewest significant figures.

Q: Are zeros always significant?

No. Leading zeros are never significant. Zeros between non-zero digits are significant. Trailing zeros after a decimal point are significant; trailing zeros in whole numbers without a decimal point are ambiguous.

Q: Does scientific notation make significant figures clearer?

Yes. In scientific notation only the coefficient's digits are significant, so 1.20 × 10³ clearly has three significant figures while 1200 is ambiguous.

Q: What happens when the next digit is exactly 5?

This calculator uses the round-half-up convention: a digit of exactly 5 (followed by no non-zero digits) causes the preceding digit to round up.