How to Round Numbers: A Complete Step-by-Step Guide

Rounding numbers becomes easy once you know which digit to keep and which digit to check. For example, 6.784 can become 6.78 when rounded to the nearest hundredth, or 7 when rounded to the nearest whole number. The target place determines the answer.

Choose the place you want to round to. Find the digit immediately to its right. If that digit is 0, 1, 2, 3, or 4, keep the target digit unchanged. If that digit is 5, 6, 7, 8, or 9, increase the target digit by 1. Remove or replace the digits after the target place.

For example, 6.784 rounded to the nearest hundredth:

• Target digit: 8
• Deciding digit: 4
• 4 is less than 5
• Keep 8 unchanged
• Result: 6.78

Rounding replaces a number with a nearby value that is easier to use or communicate.

Example: 6.784 \rightarrow 6.78.

The result depends on the selected rounding place. For a broader explanation of these concepts, read our full guide on rounding numbers explained.

The standard nearest-value rule requires looking at the deciding digit.

• 0, 1, 2, 3, 4 \rightarrow keep the target digit unchanged.
• 5, 6, 7, 8, 9 \rightarrow increase the target digit by 1.

Examples:

• 4.2 \rightarrow 4
• 4.7 \rightarrow 5
• 8.43 \rightarrow 8.4
• 8.47 \rightarrow 8.5

Clearly identify the target digit and deciding digit every time you apply this rule.

The first step is choosing the target place. You can round to the nearest whole number, nearest tenth, nearest hundredth, nearest thousandth, nearest ten, nearest hundred, nearest thousand, or nearest million.

Using the number 4,567.891:

• 4 is the thousands place.
• 5 is the hundreds place.
• 6 is the tens place.
• 7 is the ones place (nearest whole number).
• 8 is the tenths place.
• 9 is the hundredths place.
• 1 is the thousandths place.

Identify the digit that will remain.

Example: 38.476 For rounding to the nearest tenth:

• Target digit = 4
• Deciding digit = 7
• Therefore: 38.476 \rightarrow 38.5

For nearest hundredth:

• Target digit = 7
• Deciding digit = 6
• Result = 38.48

The digit immediately to the right of the target determines what happens.

When the deciding digit is 0 to 4, keep the target digit. Example: 7.43 \rightarrow 7.4

When the deciding digit is 5 to 9, increase the target digit. Example: 7.48 \rightarrow 7.5

When increasing 9 causes a carry, you apply the addition to the next digit left. Example: 4.99 \rightarrow 5.0 when rounding to the nearest tenth.

After the target digit has been determined, remove or replace the digits after the target place.

Examples:

• 6.784 \rightarrow 6.78
• 12.347 \rightarrow 12.35
• 8,476 \rightarrow 8,500

Zeros may remain when they communicate the requested place or precision.

Select the ones digit as the target and the tenths digit as the deciding digit.

Examples:

• 4.2 \rightarrow 4
• 4.5 \rightarrow 5 under Half Up
• 4.8 \rightarrow 5
• 19.3 \rightarrow 19
• 19.7 \rightarrow 20

Exact midpoint cases (like 4.5) are handled separately based on the specific rounding rule.

Examples:

• 6.72 \rightarrow 6.7 (Target 7, deciding 2)
• 6.74 \rightarrow 6.7 (Target 7, deciding 4)
• 6.75 \rightarrow 6.8 under Half Up (Target 7, deciding 5)
• 6.78 \rightarrow 6.8 (Target 7, deciding 8)

The third decimal place determines whether the hundredths digit changes.

Examples:

• 5.674 \rightarrow 5.67
• 5.675 \rightarrow 5.68 under Half Up
• 5.678 \rightarrow 5.68

Examples:

• 3.14159 \rightarrow 3.142
• 7.2344 \rightarrow 7.234
• 7.2346 \rightarrow 7.235

You can round whole numbers to the nearest ten, nearest hundred, nearest thousand, nearest ten thousand, nearest hundred thousand, or nearest million.

Examples:

• 347 \rightarrow 350 (Target 4, deciding 7)
• 342 \rightarrow 340 (Target 4, deciding 2)
• 8,475 \rightarrow 8,500 under Half Up (Target 4, deciding 7)
• 8,421 \rightarrow 8,400 (Target 4, deciding 2)
• 12,650 \rightarrow 13,000 under Half Up (Target 2, deciding 6)

Leading zeros do not hold size magnitude, but they still occupy decimal places.

Examples:

• 0.0467 \rightarrow 0.05 to the nearest hundredth
• 0.00467 \rightarrow 0.005 to the nearest thousandth
• 0.9996 \rightarrow 1.000 to the nearest thousandth

Place value determines which digits are retained.

Examples:

• 1,249 \rightarrow 1,000
• 1,250 \rightarrow 1,300 under Half Up
• 25,678 \rightarrow 25,700
• 3,456,789 \rightarrow 3,457,000

Explain negative values using the number line. Clearly distinguish rounding to the nearest value, toward zero, away from zero, Ceiling, and Floor.

Examples:

• -2.3 \rightarrow -2
• -2.7 \rightarrow -3
• -7.4 \rightarrow -7
• -7.6 \rightarrow -8

An exact midpoint requires a specific rounding method such as Half Up, Half Down, Half Even (Banker’s Rounding), or Half Away From Zero.

Using 2.5, 3.5, 4.5, or -2.5, different methods can produce different results. Read our Banker’s Rounding guide to see exactly how these options function.

Significant figures are different from decimal places.

Examples:

• 4,567 to 2 significant figures \rightarrow 4,600
• 0.004567 to 2 significant figures \rightarrow 0.0046

Use our significant figures counter for more details.

Decimal places count digits after the decimal point. Significant figures count meaningful digits starting from the first non-zero digit. Practice these concepts at our decimal places calculator.

• Checking the wrong digit: Look right of the target.
• Changing the deciding digit instead of the target digit: Only target digits remain.
• Confusing decimal places with significant figures: Know which rule applies.
• Forgetting carry-over: Remember to push values left if needed.
• Mishandling negative numbers: Check the direction to zero.
• Assuming every 5 produces the same result: Know your tie-breaker.
• Using the wrong rounding method: Check requirements.
• Rounding intermediate calculations too early: Wait until the end.
• Double rounding: Round only once.
• Assuming software uses the same rounding rule: Check the language.

Use 3.449 as a verified example. Directly to nearest tenth: 3.4 First to nearest hundredth: 3.45 Then to nearest tenth: 3.5

This explains why double rounding can produce a different result.

Rounding creates a difference between the original and rounded value.

Example: 6.786 \rightarrow 7 Absolute error: |7 - 6.786| = 0.214

Read more with our guide on rounding error explained.

For nearest-value rounding to an increment d, the maximum absolute error = d / 2.

Examples:

• nearest whole number \rightarrow 0.5
• nearest tenth \rightarrow 0.05
• nearest hundredth \rightarrow 0.005

This bound applies to nearest-value rounding and not automatically to Ceiling or Floor methods.

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The Rounding Calculator allows you to:

1. Enter the number.
2. Select what to round to.
3. Select the rounding method if needed.
4. Run the calculation.
5. Review the rounded result and explanation.