Maths7 min readUpdated Mar 25, 2026

Significant Figures Rules: Complete Guide with Examples

The Calculory Team

Content and Research

Master all six rules for counting significant figures with clear examples. Learn how to apply sig fig rules in addition, multiplication, and scientific notation.

Key Takeaways

All non-zero digits are always significant. Zeros between non-zero digits (captive zeros) are always significant. Leading zeros are never significant.
Trailing zeros after a decimal point ARE significant (2.500 = 4 sig figs). Trailing zeros in whole numbers without a decimal are ambiguous (1,500 = 2, 3, or 4 sig figs).
For addition and subtraction, round to the fewest DECIMAL PLACES. For multiplication and division, round to the fewest SIGNIFICANT FIGURES. These are different rules.
A 50% increase followed by a 50% decrease does not return to the start. Similarly, subtracting two close numbers (24.57 - 24.52 = 0.05) can reduce four sig figs to one.
Scientific notation removes all ambiguity: 4.50 x 10^3 is clearly three sig figs, while 4500 could be two, three, or four.
Use the free Sig Fig Rules Calculator to count significant figures in any number and verify your manual work.

What Are Significant Figures and Why Do They Matter?

Significant figures (sig figs) are the digits in a number that carry meaningful information about the precision of a measurement. They tell you which digits are real and which are just placeholders.

Why Sig Figs Prevent False Precision

Measurement	Sig Figs	What It Communicates
152.3 cm	4	Confident about 152, best estimate on the .3
152.300000 cm	9	Implies nanometer precision (almost certainly false)
300 km	1, 2, or 3	Ambiguous: could be 298 km or 304 km
3.00 x 10^2 km	3	Unambiguous: measured to the ones place

In science, engineering, and medicine, significant figures prevent false precision from creeping into calculations. If you measure a room as 5.2 m (two sig figs) and 3.14 m (three sig figs), your area cannot have more than two sig figs.

Calculation	Calculator Shows	Correct Answer	Why
5.2 x 3.14	16.328	16	Limited by 5.2 (two sig figs)
5.20 x 3.14	16.328	16.3	Limited by both (three sig figs)
5.200 x 3.14	16.328	16.3	Still limited by 3.14 (three sig figs)

Use the Sig Fig Rules Calculator to count significant figures in any number instantly and check your answers.

The Six Rules for Counting Significant Figures

Complete Sig Fig Rules Reference

Rule	Description	Example	Sig Figs
1. Non-zero digits	Always significant	4,572	4
2. Captive zeros	Zeros between non-zero digits are significant	1,003	4
3. Leading zeros	Never significant (just placeholders)	0.0042	2
4. Trailing zeros (with decimal)	Significant (show precision)	2.500	4
5. Trailing zeros (no decimal)	Ambiguous without context	1,500	2, 3, or 4
6. Exact numbers	Infinite sig figs (never limit precision)	12 eggs, 1 m = 100 cm	Infinite

Practice: How Many Sig Figs?

Number	Sig Figs	Rule Applied	Explanation
0.00340	3	Rules 3 and 4	Leading zeros not significant; trailing zero after decimal is
50.09	4	Rules 1 and 2	Captive zero between 5 and 9 is significant
6.020 x 10^23	4	Rules 1, 2, 4	Every digit in the coefficient counts
100.	3	Rule 4	Decimal point makes trailing zeros significant
100	1 (ambiguous)	Rule 5	No decimal, so trailing zeros are ambiguous
0.00560	3	Rules 3 and 4	5, 6, and trailing 0 are significant; leading zeros are not

Confused by a number? Convert to scientific notation. If 0.00560 becomes 5.60 x 10^-3, you can clearly see three sig figs in the coefficient.

Sig Figs in Addition and Subtraction

For addition and subtraction, round your answer to the fewest decimal places found in any number. This is different from the multiplication rule.

Why Decimal Places, Not Sig Figs?

When adding, you line up decimal points. The least precise number determines where the last reliable digit falls.

Worked Examples

Calculation	Calculator Result	Limiting Value	Decimal Places	Correct Answer
12.52 + 1.7 + 0.084	14.304	1.7	1 dp	14.3
100.0 - 7.33	92.67	100.0	1 dp	92.7
25.436 + 0.31 - 7.1	18.646	7.1	1 dp	18.6
150.0 + 0.507	150.507	150.0	1 dp	150.5

The Catastrophic Cancellation Trap

Subtracting similar numbers can destroy precision:

Calculation	Input Sig Figs	Result	Result Sig Figs	Precision Lost
24.57 - 24.52	4 each	0.05	1	3 sig figs lost
9.87 - 9.92	3 each	-0.05	1	2 sig figs lost
1,000.0 - 999.7	5 and 4	0.3	1	3 sig figs lost

This is a real concern in scientific computing. If your experiment relies on the difference between two close measurements, you need high-precision instruments. Try these calculations with the Sig Fig Addition Calculator or Sig Fig Subtraction Calculator.

Sig Figs in Multiplication and Division

For multiplication and division, round your answer to the fewest significant figures found in any number used in the calculation.

Why Sig Figs, Not Decimal Places?

When multiplying, you combine magnitudes. The least precise measurement limits the overall precision of the product.

Worked Examples

Calculation	Calculator Result	Sig Figs in Each Input	Limiting Factor	Correct Answer
4.56 x 1.4	6.384	3 and 2	1.4 (2 sf)	6.4
0.0032 x 520	1.664	2 and 2	Both (2 sf)	1.7
8.40 / 2.0	4.2	3 and 2	2.0 (2 sf)	4.2
3.14159 x (2.5)^2	19.635	6 and 2	2.5 (2 sf)	20
6.022 x 10^23 x 0.050	3.011 x 10^22	4 and 2	0.050 (2 sf)	3.0 x 10^22

Common Mistake: Counting Decimal Places Instead of Sig Figs

Number	Decimal Places	Significant Figures	Which Matters for Multiplication?
0.0042	4	2	Sig figs (2)
3.00	2	3	Sig figs (3)
520	0	2 (ambiguous)	Sig figs (2)

Verify your multiplication and division results with the Sig Fig Multiplication Calculator or Sig Fig Division Calculator.

Scientific Notation and Significant Figures

Scientific notation eliminates all ambiguity about sig figs. Every digit in the coefficient is significant, and the power of 10 handles magnitude.

Ambiguous vs Unambiguous

Standard Notation	Ambiguous?	Scientific Notation	Sig Figs
4,500	Yes	4.5 x 10^3	2
4,500	Yes	4.50 x 10^3	3
4,500	Yes	4.500 x 10^3	4
0.00072	No (but confusing)	7.2 x 10^-4	2
0.000720	No	7.20 x 10^-4	3

Calculations in Scientific Notation

Operation	Calculation	Raw Result	Correct Answer	Rule Applied
Multiplication	(3.0 x 10^4) x (2.00 x 10^-2)	6.00 x 10^2	6.0 x 10^2	2 sf (from 3.0)
Division	(8.4 x 10^5) / (2.1 x 10^2)	4.0 x 10^3	4.0 x 10^3	2 sf (both have 2)
Addition	3.2 x 10^3 + 4.5 x 10^2	3.65 x 10^3	3.7 x 10^3	1 dp in 10^3 scale

Best practice for multi-step calculations: Carry one or two extra sig figs through intermediate steps and only round the final answer. This prevents rounding errors from accumulating. Use the Sig Fig Scientific Notation Calculator to convert and verify.

Tricky Cases: The Numbers That Trip Everyone Up

Leading Zeros

Zeros that only set the decimal point are never significant.

Number	Leading Zeros	Significant Digits	Sig Figs	Scientific Notation
0.0042	3 (not significant)	4, 2	2	4.2 x 10^-3
0.00560	3 (not significant)	5, 6, 0	3	5.60 x 10^-3
0.10	1 (not significant)	1, 0	2	1.0 x 10^-1

Trailing Zeros in Whole Numbers

The most ambiguous case. Without a decimal point, there is no way to know.

Number	Possible Sig Figs	How to Clarify
2,300	2, 3, or 4	Write 2.3 x 10^3 (2 sf) or 2.30 x 10^3 (3 sf) or 2.300 x 10^3 (4 sf)
1,500	2, 3, or 4	Write 1.5 x 10^3 or 1.50 x 10^3 or 1.500 x 10^3
10,000	1 to 5	Write 1 x 10^4 through 1.0000 x 10^4

Exact Numbers

Counted quantities and defined conversions have infinite sig figs and never limit your answer.

Exact Number	Type	Effect on Calculation
12 coins	Counted quantity	Does not limit sig figs
1 inch = 2.54 cm	Defined conversion	Does not limit sig figs
2 (in d = 2r)	Mathematical constant	Does not limit sig figs
pi (3.14159...)	Irrational constant	Use enough digits to exceed your measurement precision

Example: 12 coins weigh 34.2 g total. Mass per coin = 34.2 / 12 = 2.85 g (three sig figs, limited only by 34.2). The 12 is exact.

Sig Figs in Lab Reports: Chemistry and Physics Context

In science courses, sig figs directly affect your lab report grades and the validity of your conclusions.

Lab Equipment Precision Guide

Equipment	Typical Precision	Sig Figs	Example Reading
Analytical balance	0.001 g	4-5	25.432 g
Top-loading balance	0.01 g	3-4	25.43 g
Graduated cylinder (100 mL)	0.5 mL	3	45.5 mL
Volumetric flask (100 mL)	0.08 mL	4	100.0 mL
Buret (50 mL)	0.02 mL	4	23.45 mL
Stopwatch	0.01 s	3-4	1.24 s
Ruler (30 cm)	0.5 mm	3	15.2 cm

Common Lab Report Errors

Error	What Students Do	What They Should Do
Calculator dump	Report 9.7638451 m/s^2	Report 9.8 m/s^2 (2 sf from length measurement)
Not tracking through steps	Round each step independently	Carry extra digits, round only the final answer
Wrong equipment precision	Assume graduated cylinder = 4 sf	Check actual precision: graduated cylinder = 3 sf
Ignoring exact numbers	Let "2" in d=2r limit sig figs	Recognize 2 is exact (infinite sig figs)

Professors look for correct sig fig usage as evidence you understand measurement uncertainty. A numerically perfect answer with too many sig figs suggests you plugged numbers into a formula without understanding the underlying precision. Use our Chemistry Sig Fig Calculator to check your lab calculations.

Six Common Sig Fig Mistakes and How to Fix Them

Mistake-by-Mistake Reference

#	Mistake	Example	Correct Approach
1	Counting leading zeros	Saying 0.0052 has 4 sig figs	Convert to sci notation: 5.2 x 10^-3 = 2 sig figs
2	Mixing up add/multiply rules	Using sig fig rule for addition	Addition = decimal places. Multiplication = sig figs
3	Rounding mid-calculation	Rounding step 1 before step 2	Carry extra digits, round only the final answer
4	Limiting by exact numbers	Letting pi limit your answer to 6 sf	Exact and defined numbers have infinite sig figs
5	Ignoring cancellation	Not realizing 24.57 - 24.52 = 0.05 (1 sf)	Subtraction of close numbers destroys precision
6	Reporting calculator output	Writing 16.328 m^2 from 5.2 x 3.14	Answer limited by 5.2: 16 m^2 (2 sf)

Memory Trick

Addition lines up decimals (so count decimal places)
Multiplication combines magnitudes (so count sig figs)

Verify your work with the Sig Fig Rounding Calculator or the general Rounding Calculator for standard rounding.

Practice Problems with Solutions

Test your understanding. Try each problem before checking the answer.

Counting Sig Figs

#	Number	Answer	Explanation
1	0.00340	3 sf	Leading zeros not significant; trailing zero after decimal is
2	1,020	3 sf	Captive zero significant; trailing zero ambiguous (convention: not counted)
3	6.020 x 10^23	4 sf	Every coefficient digit counts: 6, 0, 2, 0
4	100.	3 sf	Decimal point makes trailing zeros significant

Calculations

#	Problem	Working	Answer
5	4.52 + 1.4	= 5.92, round to 1 dp (from 1.4)	5.9
6	3.0 x 1.25	= 3.75, round to 2 sf (from 3.0)	3.8
7	0.0045 / 2.1	= 0.002143, round to 2 sf (both have 2)	0.0021
8	150.0 + 0.507	= 150.507, round to 1 dp (from 150.0)	150.5
9	(2.34 x 10^2) x (1.5 x 10^-1)	= 3.51 x 10^1, round to 2 sf (from 1.5)	3.5 x 10^1
10	34.2 g / 12 coins	12 is exact, so 3 sf from 34.2	2.85 g per coin

Check all your practice answers with the Sig Fig Addition Calculator and Sig Fig Multiplication Calculator. Getting the right answer on paper and verifying with a calculator builds confidence for exams.

Frequently Asked Questions

How many significant figures does 0.00450 have?

Three significant figures: 4, 5, and the trailing 0. Leading zeros (0.00) are never significant because they only indicate decimal placement. The trailing zero after 5 is significant because it was deliberately included to show precision.

How many significant figures does 1000 have?

It is ambiguous without additional context. The number 1000 could have 1, 2, 3, or 4 significant figures depending on precision. To clarify, use scientific notation: 1 x 10^3 (1 sig fig), 1.0 x 10^3 (2 sig figs), 1.00 x 10^3 (3 sig figs), or 1.000 x 10^3 (4 sig figs).

What is the sig fig rule for addition and subtraction?

Round the result to the fewest decimal places of any number in the calculation. For example, 12.52 + 1.7 = 14.22, which rounds to 14.2 because 1.7 has only one decimal place. This differs from the multiplication rule, which uses fewest significant figures instead.

What is the sig fig rule for multiplication and division?

Round the result to the fewest total significant figures of any number in the calculation. For example, 4.56 x 1.4 = 6.384, which rounds to 6.4 because 1.4 has only 2 significant figures. This differs from the addition rule, which uses decimal places.

Are zeros between non-zero digits significant?

Yes, always. Zeros sandwiched between non-zero digits are called captive zeros and are always significant. The number 1002 has 4 significant figures, 50.3 has 3 significant figures, and 4007 has 4 significant figures.

Why do significant figures matter in chemistry and physics?

Significant figures communicate the precision of a measurement. Reporting a mass as 5.00 g (3 sig figs) means the balance measured to the nearest 0.01 g, while 5 g (1 sig fig) implies only nearest-gram precision. In lab reports, using too many sig figs claims false precision, while too few discards real data.

Do exact numbers have unlimited significant figures?

Yes. Exact numbers, such as counting numbers (12 eggs), defined conversions (1 inch = 2.54 cm exactly), and mathematical constants used by definition, have unlimited significant figures and never limit the precision of a calculation.

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