Significant Figures Rules

Significant figures, also called sig figs, are the digits in a number that communicate its meaningful precision. Knowing the rules for significant figures helps you determine which digits count in a measurement, calculation, or reported result.

The most important part of counting significant figures is understanding how zeros are treated. Non-zero digits are straightforward, while leading zeros, zeros between non-zero digits, and trailing zeros can have different roles.

This guide explains the significant figures rules with clear examples, including decimal numbers, whole numbers, exact numbers, and scientific notation.

If you are new to the topic, start with our guide to What Are Significant Figures?

Significant Figures Rules at a Glance

Rule 1: All Non-Zero Digits Are Significant

Every non-zero digit from 1 through 9 is significant.

There are no placeholder zeros involved, so these numbers are straightforward to count.

Examples:

• 7 → 1 significant figure

• 42 → 2 significant figures

• 583 → 3 significant figures

• 12.345 → 5 significant figures

For example:

583.2

contains four significant figures because all four digits are non-zero.

Rule 2: Zeros Between Non-Zero Digits Are Significant

A zero located between non-zero digits is significant. These are sometimes called captive zeros or embedded zeros.

Examples:

• 101 → 3 significant figures

• 1002 → 4 significant figures

• 2.05 → 3 significant figures

• 3.004 → 4 significant figures

For example:

1002

contains four significant figures:

1, 0, 0, and 2.

The zeros are between non-zero digits, so they count.

Rule 3: Leading Zeros Are Not Significant

Leading zeros are zeros that appear before the first non-zero digit. They are used to position the decimal point and do not indicate additional precision.

Examples:

• 0.5 → 1 significant figure

• 0.05 → 1 significant figure

• 0.0052 → 2 significant figures

• 0.000725 → 3 significant figures

For example:

0.00450

The leading zeros do not count. The significant digits are:

4, 5, and 0

Therefore, 0.00450 has 3 significant figures.

The same principle applies when there are zeros before a whole number:

00042

has 2 significant figures, because the leading zeros are not significant.

Rule 4: Trailing Zeros in Decimal Numbers Are Significant

A trailing zero is a zero at the end of a number.

When trailing zeros appear after a decimal point, they are significant because their written form can communicate the precision of the value.

Examples:

• 2.0 → 2 significant figures

• 2.50 → 3 significant figures

• 4.500 → 4 significant figures

• 0.0400 → 3 significant figures

For example:

4.500

has four significant figures:

4, 5, 0, and 0.

The zeros after the decimal point are part of the stated precision.

Rule 5: Trailing Zeros in Whole Numbers Can Be Ambiguous

Trailing zeros at the end of a whole number without a decimal point can be ambiguous.

For example:

1500

does not, by itself, clearly communicate whether the intended precision is 2, 3, or 4 significant figures.

Scientific notation can remove this ambiguity:

• 1.5 × 10³ → 2 significant figures

• 1.50 × 10³ → 3 significant figures

• 1.500 × 10³ → 4 significant figures

This is why scientific notation is useful when the number of significant figures needs to be communicated clearly.

NIST similarly notes that a value such as 1200 m does not by itself make the significance of the final zeros clear, while a form such as 1.200 km communicates four significant digits.

Rule 6: Exact Numbers Are Different From Measured Values

Exact numbers come from counting or from definitions rather than from a measurement with limited precision.

Examples include:

• 12 students

• 24 eggs

• 3 cars

The number 12 in “12 students” is an exact count, so it is not limited by measurement precision.

Defined relationships can also be treated as exact within the relevant system or convention.

For example, the relationship:

1 inch = 2.54 centimeters

is an exact definition.

This is different from a measured value such as:

2.54 cm

obtained from an instrument, where the reported digits depend on the measurement and its precision.

Rule 7: Scientific Notation Makes Significant Figures Clear

Scientific notation expresses a number as a coefficient multiplied by a power of 10.

For example:

4.50 × 10³

The coefficient is 4.50, which contains 3 significant figures.

The exponent does not count as a significant figure.

Examples:

• 2 × 10⁵ → 1 significant figure

• 2.5 × 10⁵ → 2 significant figures

• 2.50 × 10⁵ → 3 significant figures

• 2.500 × 10⁵ → 4 significant figures

Scientific notation is especially useful for very large or very small numbers because it makes the intended precision explicit.

How to Count Significant Figures

Use this simple process:

Step 1: Find the first non-zero digit

Start counting at the first non-zero digit.

Step 2: Count all significant digits after it

Count non-zero digits and any zeros that are between significant digits or are significant trailing zeros.

Step 3: Ignore leading zeros

Do not count zeros before the first non-zero digit.

Step 4: Check trailing zeros

Determine whether the trailing zeros are clearly significant from the decimal notation or context.

Example

How many significant figures are in:

0.005060

Ignore the leading zeros.

The significant digits are:

5, 0, 6, 0

Therefore:

0.005060 has 4 significant figures.

Examples of Significant Figures

Example 1: 347

All digits are non-zero.

347 → 3 significant figures

Example 2: 0.0068

The zeros before 6 are leading zeros.

0.0068 → 2 significant figures

Example 3: 205

The zero is between two non-zero digits.

205 → 3 significant figures

Example 4: 0.0300

The leading zeros do not count, but the two trailing zeros after the decimal point do.

0.0300 → 3 significant figures

Example 5: 500

Without additional context, the number of significant figures is ambiguous.

Scientific notation can clarify it:

• 5 × 10² → 1 significant figure

• 5.0 × 10² → 2 significant figures

• 5.00 × 10² → 3 significant figures

Example 6: 7.040

The zero between 7 and 4 is significant, and the final zero after the decimal is also significant.

7.040 → 4 significant figures

A Quick Way to Remember the Zero Rules

When you see zeros, ask where they are located.

Before the first non-zero digit?
Usually not significant.

Between non-zero digits?
Significant.

At the end after a decimal point?
Significant.

At the end of a whole number without a decimal point?
Potentially ambiguous; use context or scientific notation.

This simple check resolves most significant-figure questions.

Significant Figures in Measurements

Significant figures are commonly used when reporting measured quantities because the written digits communicate the precision of the reported value.

For example:

15.4 mL

communicates different precision from:

15.40 mL

The second value includes an additional significant digit.

However, significant figures should not be confused with uncertainty. The number of significant figures is one way of communicating precision, while measurement uncertainty provides a more explicit description of the possible variation associated with a measurement.

Significant Figures and Rounding

Counting significant figures tells you how many meaningful digits a number contains. Rounding significant figures determines how to reduce a number to a specified number of significant figures.

For example:

8.746

rounded to 3 significant figures becomes:

8.75

The first three significant digits are 8, 7, and 4. The next digit is 6, so the final retained digit increases by one.

For detailed rounding examples, see our guide to Rounding Significant Figures.

Significant Figures in Calculations

The rules for identifying significant figures are different from the rules used to report results from calculations.

For multiplication and division, the result is generally reported using the number of significant figures in the input with the fewest significant figures.

Example:

4.5 × 2.13 = 9.585

Because 4.5 has 2 significant figures, the result is generally reported as:

9.6

For addition and subtraction, the result is generally determined by the least precise decimal place rather than by the number of significant figures.

Example:

12.11 + 0.3 = 12.41

The least precise value is 0.3, so the result is reported as:

12.4

When a specific course, laboratory procedure, or professional standard gives different instructions, follow those instructions.

Common Mistakes With Significant Figures

Counting leading zeros

Incorrect:

0.0045 → 4 significant figures

Correct:

0.0045 → 2 significant figures

Ignoring captive zeros

Incorrect:

1002 → 2 significant figures

Correct:

1002 → 4 significant figures

Treating every trailing zero as significant

A whole number such as 1500 may be ambiguous without additional information.

Use scientific notation when you need to communicate the intended precision clearly.

Confusing significant figures with decimal places

These are not the same thing.

For example:

0.00450

has:

• 3 significant figures

• 5 decimal places

Rounding before identifying the required precision

First determine how many significant figures are required. Then round the number according to the applicable rounding rule.

Significant Figures Rules: Quick Reference

Remember these core rules:

1. Non-zero digits are always significant.

2. Zeros between non-zero digits are significant.

3. Leading zeros are not significant.

4. Trailing zeros after a decimal point are significant.

5. Trailing zeros in whole numbers can be ambiguous without context.

6. Exact counted values are not limited by measurement precision.

7. Scientific notation can make the intended number of significant figures explicit.

Understanding these rules makes it much easier to count significant figures correctly and report numerical results consistently.

Check Your Significant Figures

If you want to check the number of significant figures in a value or perform a supported calculation, use our Significant Figures Calculator.

For more information about the concept itself, read What Are Significant Figures?

If your main goal is to reduce a number to a specific number of significant figures, see Rounding Significant Figures.

Frequently Asked Questions

What are the main rules for significant figures?

The main rules are that non-zero digits are significant, zeros between non-zero digits are significant, leading zeros are not significant, and trailing zeros after a decimal point are significant. Trailing zeros in whole numbers can be ambiguous without additional context.

Are zeros between non-zero digits significant?

Yes. Zeros between non-zero digits are significant.

For example, 1002 has 4 significant figures.

Are leading zeros significant?

No. Leading zeros only help position the decimal point.

For example, 0.0045 has 2 significant figures.

Are trailing zeros significant?

It depends on how the number is written and the context. Trailing zeros after a decimal point are significant, while trailing zeros in whole numbers without a decimal point can be ambiguous.

How many significant figures are in 0.005060?

There are 4 significant figures: 5, 0, 6, and 0.

How many significant figures are in 1000?

The written number 1000 is ambiguous without additional context. Scientific notation can make the intended precision clear:

• 1 × 10³ → 1 significant figure

• 1.0 × 10³ → 2 significant figures

• 1.00 × 10³ → 3 significant figures

• 1.000 × 10³ → 4 significant figures

What is the difference between significant figures and decimal places?

Significant figures count meaningful digits beginning with the first non-zero digit. Decimal places count the digits appearing after the decimal point.

For example, 0.00450 has 3 significant figures but 5 decimal places.

Do exact numbers have significant figures?

Exact numbers are not limited by measurement precision. Examples include counted quantities such as 12 students or defined relationships.

Why is scientific notation useful for significant figures?

Scientific notation makes the intended precision clear by showing exactly which digits are significant in the coefficient.

How can I check significant figures quickly?

You can use our Significant Figures Calculator to check a value and perform supported significant-figure calculations.