Significant Figures vs Decimal Places

Significant figures and decimal places are both used to describe numerical precision, but they are not the same thing.

Significant figures count meaningful digits in a number, while decimal places count the digits appearing to the right of the decimal point.

Understanding the difference is particularly important when performing calculations because addition and subtraction generally use decimal places, while multiplication and division generally use significant figures.

If you are new to the subject, start with What Significant Figures Tell You About a Number before comparing the two concepts.

What Are Significant Figures?

Significant figures are the digits in a number that communicate meaningful information about its precision.

For example:

4.52

contains 3 significant figures.

The digits 4, 5, and 2 are all significant.

However, not every zero in a number is automatically significant. Leading zeros, captive zeros, and trailing zeros can have different meanings depending on their position and notation.

For the complete rules, see Significant Figures Rules.

What Are Decimal Places?

Decimal places refer only to the number of digits located to the right of the decimal point.

For example:

12.345

has:

• 3 decimal places

• 5 significant figures

Another example:

7.20

has:

• 2 decimal places

• 3 significant figures

The two concepts therefore measure different things.

Significant Figures vs Decimal Places

The simplest distinction is:

Significant figures count meaningful digits throughout a number, while decimal places count digits after the decimal point.

Consider:

0.00450

This number has:

• 2 decimal places? No — it has 5 digits after the decimal point

• 3 significant figures — 4, 5, and the final 0

This example demonstrates why significant figures and decimal places cannot be used interchangeably.

Quick Comparison

The number of decimal places can be greater than, equal to, or less than the number of significant figures.

Why Are They Different?

Decimal places are determined simply by looking at the position of the decimal point.

Significant figures require you to determine which digits carry meaningful precision.

For example:

0.0032

has four digits after the decimal point, so it has:

4 decimal places

But the leading zeros are not significant.

Therefore:

0.0032 has 2 significant figures.

This is one of the most common reasons people confuse the two concepts.

Leading Zeros and Decimal Places

Leading zeros are zeros that appear before the first non-zero digit.

For example:

0.0056

has:

• 4 decimal places

• 2 significant figures

The three zeros before 56 are not significant.

They only indicate where the decimal point is located.

This distinction becomes especially important when working with very small measurements.

Captive Zeros

Zeros between non-zero digits are significant.

For example:

2.05

has:

• 2 decimal places

• 3 significant figures

The zero is between 2 and 5, so it counts as a significant figure.

Another example:

1002

has:

• 0 decimal places

• 4 significant figures

There are no digits after the decimal point, but all four digits are significant because the zeros occur between non-zero digits.

Trailing Zeros

Trailing zeros can communicate precision, particularly when they appear after a decimal point.

For example:

6.0

has:

• 1 decimal place

• 2 significant figures

6.00

has:

• 2 decimal places

• 3 significant figures

The additional zeros communicate that the number has been recorded to a finer decimal precision.

However, trailing zeros in whole numbers can be ambiguous without additional notation.

For example:

500

does not clearly communicate whether the intended precision is 1, 2, or 3 significant figures.

Scientific notation can remove this ambiguity:

• 5 × 10² → 1 significant figure

• 5.0 × 10² → 2 significant figures

• 5.00 × 10² → 3 significant figures

Decimal Places in Addition and Subtraction

Decimal places become particularly important when adding or subtracting measured values.

For addition and subtraction, the result is generally reported to the same number of decimal places as the value with the fewest decimal places.

Example

Calculate:

12.35 + 4.2

First calculate:

12.35 + 4.2 = 16.55

Now look at the decimal places:

• 12.35 → 2 decimal places

• 4.2 → 1 decimal place

The final answer should therefore have 1 decimal place:

16.6

Notice that we did not determine the answer by counting significant figures.

For more examples, see Significant Figures in Addition and Subtraction.

Significant Figures in Multiplication and Division

Multiplication and division generally use a different rule.

The final result is reported with the same number of significant figures as the input value with the fewest significant figures.

Example

Calculate:

4.52 × 2.1

Significant figures:

• 4.52 → 3 significant figures

• 2.1 → 2 significant figures

Calculate:

4.52 × 2.1 = 9.492

The result should contain 2 significant figures:

9.5

Here, decimal places are not the determining factor.

For more examples, see Significant Figures in Multiplication and Division.

A Simple Way to Remember the Difference

Use this basic rule:

Addition and Subtraction

Think:

Decimal places

Example:

10.25 + 2.3 = 12.6

The answer is limited to one decimal place.

Multiplication and Division

Think:

Significant figures

Example:

10.25 × 2.3 = 23.575

The answer is limited to 2 significant figures:

24

The two operations therefore require different approaches.

Significant Figures and Decimal Places in Rounding

Rounding can be performed using either significant figures or decimal places, depending on what the problem asks for.

Rounding to Decimal Places

Suppose you need to round:

8.736

to 2 decimal places.

Keep:

8.73

Look at the next digit:

6

Because the next digit is 5 or greater, round the final retained digit upward:

8.74

Rounding to Significant Figures

Now round the same number to 2 significant figures.

Starting with:

8.736

The first two significant digits are 8 and 7.

The next digit is 3, so no upward rounding is required.

Therefore:

8.7

These are different results because the rounding targets are different.

For a complete explanation of rounding rules, see Rounding Significant Figures.

Example: Same Number, Different Rounding

Consider:

0.004567

To 2 decimal places

The result is:

0.00

This is technically two decimal places, but it no longer communicates the original non-zero precision in a useful way.

To 2 significant figures

The result is:

0.0046

This preserves two meaningful digits.

This example shows why significant figures are often more useful when expressing the precision of very small or very large measurements.

How Scientific Notation Helps

Scientific notation provides a convenient way to make significant figures clear.

For example:

0.0004500

can be written as:

4.500 × 10⁻⁴

The coefficient 4.500 contains:

4 significant figures

The exponent does not count as a significant figure.

Scientific notation is therefore useful when numbers contain many leading or trailing zeros.

For more detail, see Scientific Notation and Significant Figures.

Significant Figures vs Decimal Places in Measurements

When reporting measurements, significant figures can communicate the precision of the recorded value.

For example:

15.2 cm

contains:

• 1 decimal place

• 3 significant figures

While:

15.20 cm

contains:

• 2 decimal places

• 4 significant figures

The second measurement communicates a finer reported precision.

However, the number of digits you should record should be supported by the measurement method and instrument.

A calculator cannot create measurement precision that was not present in the original measurement.

For more information about measurements and reported precision, see Significant Figures in Measurements.

Common Mistakes

Mistake 1: Treating Decimal Places as Significant Figures

A number can have many decimal places but only a few significant figures.

For example:

0.00052

has:

• 5 decimal places

• 2 significant figures

Mistake 2: Counting Leading Zeros

Leading zeros do not normally count as significant figures.

0.0034

contains 2 significant figures.

Mistake 3: Using Significant Figures for Addition

For addition and subtraction, the normal rule is based on decimal places.

Mistake 4: Using Decimal Places for Multiplication

For multiplication and division, the normal rule is based on significant figures.

Mistake 5: Assuming More Decimal Places Always Means More Significant Figures

For example:

0.0001

has 4 decimal places but only 1 significant figure.

Mistake 6: Ignoring Ambiguous Trailing Zeros

A whole number such as 500 may not clearly communicate its intended significant figures.

Scientific notation can make the precision explicit.

Quick Reference: Which Rule Should You Use?

This table is a useful quick reference when solving problems involving measured values.

How to Decide Which One to Use

When a problem gives you a specific instruction, follow that instruction.

If the problem asks:

“Round to 3 decimal places”

you count digits after the decimal point.

If it asks:

“Round to 3 significant figures”

you count meaningful digits beginning with the first non-zero digit.

If you are performing a calculation:

• Addition → generally use decimal places

• Subtraction → generally use decimal places

• Multiplication → generally use significant figures

• Division → generally use significant figures

When you are unsure, identify the operation first and then apply the appropriate rule.

Practice Examples

Example 1

How many significant figures are in:

0.00620

Answer:

3 significant figures

The leading zeros are not significant, but 6, 2, and the trailing zero are significant.

The number has 5 decimal places.

Example 2

How many decimal places are in:

14.507

Answer:

3 decimal places

The number contains 5 significant figures.

Example 3

Round:

25.678

to 3 decimal places.

Answer:

25.678

It already contains 3 decimal places.

Example 4

Round:

25.678

to 3 significant figures.

Answer:

25.7

The first three significant digits are 2, 5, and 6. The next digit is 7, so the final digit rounds upward.

Example 5

Calculate:

12.4 + 3.25

The calculation gives:

15.65

The first value has 1 decimal place and the second has 2.

Therefore:

15.7

Example 6

Calculate:

12.4 × 3.25

The calculation gives:

40.3

The first value has 3 significant figures and the second also has 3.

Therefore:

40.3

Frequently Asked Questions

Are significant figures and decimal places the same?

No. Significant figures count meaningful digits in a number, while decimal places count digits to the right of the decimal point.

Is 0.0045 two significant figures?

Yes. 0.0045 contains 2 significant figures: 4 and 5. It has 4 decimal places.

Is 12.30 four significant figures?

Yes. 12.30 contains 4 significant figures and 2 decimal places.

Which is more important, significant figures or decimal places?

Neither is universally more important. They serve different purposes. The appropriate one depends on the calculation or reporting requirement.

Do leading zeros count as significant figures?

No. Leading zeros normally only indicate the position of the decimal point.

Do trailing zeros count as significant figures?

Trailing zeros after a decimal point are significant. Whole-number trailing zeros can be ambiguous without additional notation.

Which rule is used for addition and subtraction?

Addition and subtraction generally use the value with the fewest decimal places to determine the precision of the final result.

Which rule is used for multiplication and division?

Multiplication and division generally use the value with the fewest significant figures.

Why can a number have more decimal places than significant figures?

Because leading zeros count as decimal places but are not significant figures.

For example, 0.0032 has 4 decimal places but only 2 significant figures.

How do I round to significant figures?

Start counting at the first non-zero digit, keep the requested number of significant digits, and use the next digit to determine whether rounding is required.

How do I round to decimal places?

Count digits from the decimal point, keep the requested number of places, and use the next digit to determine whether rounding is required.

Can scientific notation make significant figures clearer?

Yes. Scientific notation makes the significant digits explicit and is especially useful for numbers containing many zeros.

Can I check my answer with a calculator?

Yes. You can use the Significant Figures Calculator to check supported calculations. Remember that a calculator performs the arithmetic; you still need to apply the appropriate precision rule.

Final Takeaway

Significant figures and decimal places are related, but they answer different questions.

Decimal places tell you how many digits are written after the decimal point.

Significant figures tell you how many meaningful digits are being reported.

For calculations, remember:

Addition and subtraction → decimal places

Multiplication and division → significant figures

Once you understand this distinction, many significant-figure problems become much easier to solve and report correctly.