Rounding Significant Figures

Rounding significant figures means reducing a number to a specified number of meaningful digits while keeping the value as close as possible to the original number.

Significant-figure rounding is commonly used when reporting measurements and calculated results in chemistry, physics, engineering, laboratory work, and other fields where precision matters.

The key is to identify the required number of significant figures, look at the next digit, and then decide whether the last retained digit needs to be increased.

If you first need to understand how significant figures are identified, see our guide to What Are Significant Figures?

How to Round to Significant Figures

Follow these steps when rounding a number to a specified number of significant figures.

Step 1: Find the first significant digit

Start with the first non-zero digit in the number.

Leading zeros are not significant.

For example:

0.004583

The first significant digit is 4.

Step 2: Count the required significant figures

Count from the first significant digit until you reach the number of significant figures required.

For example, to round 0.004583 to 3 significant figures:

4, 5, 8

These are the three digits that will initially be retained.

Step 3: Look at the next digit

Look at the digit immediately after the last significant digit you are keeping.

• If the next digit is less than 5, leave the last retained digit unchanged.

• If the next digit is 5 or greater, increase the last retained digit by 1.

Step 4: Remove or adjust the remaining digits

After rounding, remove unnecessary digits or replace them with zeros when the number requires them.

The result should contain the requested number of significant figures.

Rounding Rule

The basic rounding rule is:

Next digit less than 5: keep the last retained digit unchanged.

Next digit 5 or greater: increase the last retained digit by 1.

Example

Round 47.32 to 3 significant figures.

The first three significant digits are:

4, 7, 3

The next digit is 2.

Because 2 is less than 5, the 3 remains unchanged.

47.32 → 47.3

Examples of Rounding Significant Figures

Example 1: Round 583.7 to 3 significant figures

The first three significant digits are 5, 8, and 3.

The next digit is 7, so the 3 increases to 4.

583.7 → 584

The result has 3 significant figures.

Example 2: Round 24.63 to 3 significant figures

The first three significant digits are 2, 4, and 6.

The next digit is 3, which is less than 5.

24.63 → 24.6

Example 3: Round 0.006784 to 3 significant figures

Ignore the leading zeros.

The first three significant digits are 6, 7, and 8.

The next digit is 4, so no rounding up is needed.

0.006784 → 0.00678

Example 4: Round 0.009876 to 2 significant figures

The first two significant digits are 9 and 8.

The next digit is 7, so the 8 increases by 1.

0.009876 → 0.0099

The result contains 2 significant figures.

Rounding Numbers With Zeros

Zeros require special attention because some zeros are significant and others are only placeholders.

Leading zeros

Leading zeros are not significant.

For example:

0.000725

To round to 2 significant figures:

• Significant digits: 7 and 2

• Next digit: 5

Therefore:

0.000725 → 0.00073

Trailing zeros after a decimal point

Trailing zeros written after a decimal point can be significant.

For example:

5.6780

Rounded to 4 significant figures:

5.678

The final zero was beyond the requested precision and is removed.

Rounding Whole Numbers

Rounding whole numbers can become ambiguous when zeros appear at the end.

For example:

1500

does not necessarily communicate how many significant figures are intended.

Scientific notation makes the precision clearer:

• 1.5 × 10³ → 2 significant figures

• 1.50 × 10³ → 3 significant figures

• 1.500 × 10³ → 4 significant figures

When the intended precision matters, scientific notation is often the clearest way to express the rounded result.

Rounding When the Next Digit Is 5

A common basic rule is to round the retained digit upward when the next digit is 5 or greater.

For example:

2.35 → 2.4 when rounded to 2 significant figures.

However, some statistical, numerical, or software contexts use different tie-breaking conventions, such as round-half-to-even. If a textbook, laboratory procedure, calculator, or professional standard specifies a particular convention, follow that convention.

For ordinary significant-figure exercises, use the rounding convention required by your course or instructions.

Rounding When Several Digits Follow

Only the first discarded digit is needed to determine the ordinary rounding direction.

For example:

4.376

Rounded to 3 significant figures:

• Retain 4, 3, and 7

• Next digit is 6

• Round 7 upward

4.376 → 4.38

The digits after the 6 do not change the direction of the ordinary rounding decision.

Rounding Across 9s

Sometimes rounding causes one or more digits to become zero and increases the digit to the left.

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 a carry.

9.98 → 10

Because 10 can be ambiguous, scientific notation can show the intended precision:

1.0 × 10¹

This clearly communicates 2 significant figures.

Rounding to 1 Significant Figure

To round to 1 significant figure, retain only the first significant digit and use the next digit to determine whether it should increase.

Example

63.4

The first significant digit is 6.

The next digit is 3, which is less than 5.

63.4 → 60

Scientific notation can make the precision explicit:

6 × 10¹

Another example:

78.2

The next digit after 7 is 8, so round upward:

78.2 → 80

To clearly communicate 1 significant figure:

8 × 10¹

Rounding to 2 Significant Figures

Example

Round 345.6 to 2 significant figures.

Retain:

3 and 4

The next digit is 5, so increase 4 to 5.

345.6 → 350

Scientific notation can make the intended precision clear:

3.5 × 10²

Rounding to 3 Significant Figures

Example

Round 12.678 to 3 significant figures.

Retain:

1, 2, and 6

The next digit is 7, so increase 6 to 7.

12.678 → 12.7

Rounding in Scientific Notation

Scientific notation is useful when rounding very large or very small numbers.

For example:

6.784 × 10⁵

Rounded to 3 significant figures:

6.78 × 10⁵

If rounded to 2 significant figures:

6.8 × 10⁵

The exponent does not count as a significant figure. The significant figures are determined by the digits in the coefficient.

Significant Figures vs Decimal Places

Do not confuse significant figures with decimal places.

Significant figures count meaningful digits starting with the first non-zero digit.

Decimal places count digits after the decimal point.

For example:

0.00450

has:

• 3 significant figures

• 5 decimal places

A number can therefore be rounded to a specified number of significant figures without being rounded to the same number of decimal places.

For more information, see our guide to What Are Significant Figures?

Rounding in Calculations

Rounding rules depend on the type of calculation.

Addition and subtraction

For addition and subtraction, the final result is generally rounded to the least precise decimal place among the values being combined.

Example:

12.11 + 0.3 = 12.41

The least precise value is 0.3, which is precise to the tenths place.

Therefore:

12.41 → 12.4

Multiplication and division

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

Example:

4.5 × 2.13 = 9.585

The value 4.5 has 2 significant figures, so the result is reported to 2 significant figures:

9.585 → 9.6

When performing multi-step calculations, avoid unnecessary rounding of intermediate results. Keep additional digits where appropriate and round the final result according to the required precision.

Common Rounding Mistakes

Mistake 1: Counting leading zeros as significant

In 0.00452, the leading zeros are not significant.

The number has 3 significant figures.

Mistake 2: Looking at the wrong digit

When rounding, the digit immediately after the last retained significant digit determines whether ordinary rounding is required.

Mistake 3: Confusing decimal places with significant figures

Rounding to 3 significant figures is not the same as rounding to 3 decimal places.

Mistake 4: Ignoring ambiguous trailing zeros

A result such as 1500 may not clearly communicate its precision. Scientific notation can make the intended number of significant figures explicit.

Mistake 5: Rounding every intermediate calculation

Premature rounding can introduce additional rounding error in multi-step calculations.

Mistake 6: Assuming every context uses the same tie-breaking convention

Most introductory significant-figure exercises use the ordinary rule of rounding up when the next digit is 5 or greater, but some numerical methods use other conventions. Follow the instructions relevant to your calculation.

ISO 80000-1 and Rounding

ISO 80000-1:2022, Quantities and units — Part 1: General, includes guidance on the rounding of numbers in Annex B. The standard describes rounding approaches used when numerical values need to be expressed with an appropriate level of precision. For significant-figure calculations, the exact rounding convention can depend on the context, such as scientific, educational, laboratory, or technical requirements. When a specific standard, textbook, laboratory procedure, or professional guideline is provided, follow its stated rounding convention. For general examples on this page, we use the commonly taught significant-figure rounding method and explain each step clearly.

Rounding Significant Figures Calculator

If you want to check a rounding result quickly, use our Significant Figures Calculator.

Enter the number exactly as it appears in your problem or measurement and select the required precision supported by the calculator.

The calculator can help you check significant figures and rounding without manually counting every digit.

For a detailed explanation of how the calculator works, see How It Works.

Frequently Asked Questions

How do you round to significant figures?

Find the first significant digit, count the required number of significant figures, and then examine the next digit. If that digit is less than 5, leave the retained digit unchanged. If it is 5 or greater, increase the retained digit by 1.

What happens if the next digit is 5?

Under the common introductory rounding rule, a next digit of 5 or greater causes the last retained digit to increase by 1. Some numerical contexts use different tie-breaking conventions.

How do you round 0.004567 to 3 significant figures?

The first three significant digits are 4, 5, and 6. The next digit is 7, so the 6 becomes 7.

0.004567 → 0.00457

How do you round 9.98 to 2 significant figures?

The next digit is 8, so rounding produces:

9.98 → 10

Scientific notation makes the precision explicit:

1.0 × 10¹

Is rounding to significant figures the same as rounding to decimal places?

No. Significant figures count meaningful digits, while decimal places count digits after the decimal point.

Should I round intermediate results?

Usually, avoid unnecessary intermediate rounding. Retaining additional digits during intermediate calculations can reduce accumulated rounding error. Round the final result according to the applicable sig fig rules or instructions.

Summary

To round a number to significant figures:

1. Find the first significant digit.

2. Count the required number of significant figures.

3. Look at the next digit.

4. If the next digit is less than 5, keep the last retained digit unchanged.

5. If the next digit is 5 or greater, increase the last retained digit by 1 under the common rounding convention.

6. Remove or adjust the remaining digits.

7. Use scientific notation when necessary to make the intended precision clear.

If you want to check a result, use our Significant Figures Calculator or read What Are Significant Figures? for a broader explanation of significant-figure rules.