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Rounding Rules

The complete guide to all rounding rules and when to use them

The Universal Rounding Rule

The 5 Rule (Standard Rounding)

If the digit is 5 or greater (5, 6, 7, 8, 9):

Round UP ⬆️

If the digit is less than 5 (0, 1, 2, 3, 4):

Round DOWN ⬇️

This is the fundamental rounding rule taught in schools worldwide. Also known as "round half up" or "standard rounding," it's used in most mathematical and everyday applications.

Basic Rounding Examples

Round UP Examples

3.5 → 4 (5 rounds up)

3.6 → 4 (6 rounds up)

3.7 → 4 (7 rounds up)

3.8 → 4 (8 rounds up)

3.9 → 4 (9 rounds up)

Round DOWN Examples

3.0 → 3 (0 rounds down)

3.1 → 3 (1 rounds down)

3.2 → 3 (2 rounds down)

3.3 → 3 (3 rounds down)

3.4 → 3 (4 rounds down)

Rounding to Different Place Values

Rounding to Nearest Ten

Look at the ones digit:

23 → 20 (3 < 5, round down)

27 → 30 (7 ≥ 5, round up)

45 → 50 (5 = 5, round up)

Rounding to Nearest Hundred

Look at the tens digit:

234 → 200 (3 < 5, round down)

567 → 600 (6 ≥ 5, round up)

850 → 900 (5 = 5, round up)

Rounding to Nearest Tenth (1 decimal)

Look at the hundredths digit:

3.14 → 3.1 (4 < 5, round down)

3.17 → 3.2 (7 ≥ 5, round up)

3.15 → 3.2 (5 = 5, round up)

Rounding to Nearest Hundredth (2 decimals)

Look at the thousandths digit:

3.142 → 3.14 (2 < 5, round down)

3.147 → 3.15 (7 ≥ 5, round up)

3.145 → 3.15 (5 = 5, round up)

Alternative Rounding Rules

1. Bankers' Rounding (Round Half to Even)

When the digit is exactly 5, round to the nearest even number. This reduces bias in statistical calculations.

2.5 → 2 (round to even)

3.5 → 4 (round to even)

4.5 → 4 (round to even)

5.5 → 6 (round to even)

Used in: Banking, statistics, IEEE 754 floating-point standard, Python's round()

2. Round Half Down

When the digit is exactly 5, round DOWN. Less common but used in specific applications.

2.5 → 2

3.5 → 3

4.5 → 4

3. Ceiling (Always Round Up)

Always round UP to the next value, regardless of the digit.

3.1 → 4

3.5 → 4

3.9 → 4

Used in: Inventory (can't order 0.7 boxes), staffing, project planning

4. Floor (Always Round Down)

Always round DOWN, removing all decimals (truncate).

3.1 → 3

3.5 → 3

3.9 → 3

Used in: Age calculations, completed years, conservative estimates

When to Use Each Rounding Rule

Rounding RuleWhen to UseExample
Standard (5 up)General math, school, everyday useTest scores, measurements
Bankers' RoundingStatistics, banking, reduce biasFinancial calculations
Always Up (Ceiling)Inventory, staffing, materials47.3 boxes → 48 boxes
Always Down (Floor)Age, years of service12.9 years old → 12 years

Common Rounding Mistakes

❌ Mistake #1: Looking at the Wrong Digit

Wrong: To round 347 to the nearest hundred, looking at the 4

Right: Look at the tens digit (4), which tells you to round down to 300

❌ Mistake #2: Rounding Multiple Times

Wrong: Round 3.456 → 3.46 → 3.5 (double rounding changes the result!)

Right: Round 3.456 → 3.5 directly (one-step rounding)

❌ Mistake #3: Forgetting That 5 Rounds Up

Wrong: Thinking 2.5 rounds down to 2

Right: 2.5 rounds UP to 3 (in standard rounding)

❌ Mistake #4: Rounding Before Calculating

Wrong: Round intermediate values during calculations (loses precision)

Right: Keep full precision, only round the final answer

Quick Reference Guide

The Golden Rule

5+ goes UP ⬆️

<5 goes DOWN ⬇️

Which Digit?

Look at the digit RIGHT AFTER the place you're rounding to

To Nearest 10

Check the ones digit

27 → 30

To Nearest 100

Check the tens digit

567 → 600

To 1 Decimal

Check the hundredths

3.17 → 3.2

To 2 Decimals

Check the thousandths

3.147 → 3.15