Rounding in Math: Definition, Rules & Examples

Definitionnoun

What is rounding in math?

Rounding replaces a number with a nearby number that is easier to use, to a chosen place value. Look at the digit immediately to the right of that place: 5 or more rounds up, 4 or less rounds down. So 47 rounds to 50 to the nearest ten, and 3.68 rounds to 3.7 to the nearest tenth.

In Spanish: redondeo
Also called: round off, rounding off, round to the nearest
Grade level: K-5

Grade 3Grade 4Grade 5Grade 6CCSS 3.NBT.A.1CCSS 4.NBT.A.3CCSS 5.NBT.A.4GED

Rounding in a picture

Rounding finds the closer of two neighbors: 263 is nearer 260, and 5.86 is nearer 5.9. The digit just to the right of the rounding place tells you which side of halfway you are on.

Formal definition and notation

To round a number to a given place, find the digit in that place (the rounding digit) and look at the digit immediately to its right. If that digit is 0 to 4, keep the rounding digit (round down); if it is 5 to 9, add 1 to the rounding digit (round up), carrying if it was 9. Then replace every digit to the right with 0 for whole-number places, or drop them after the decimal point. The result is the multiple of that place value closest to the number; a number exactly halfway, such as 45 to the nearest ten, rounds up under this rule.

Symbol	Read it as	Meaning
≈	is approximately equal to	shows a rounded value: 3.68 ≈ 3.7
to the nearest ten	to the nearest ten	the answer must be a multiple of 10, such as 260 or 270

Key facts

On a number line, rounding picks the closer of the two multiples: 263 is between 260 and 270 and closer to 260.
Only one digit decides: 149 rounds to 100 to the nearest hundred, because the tens digit is 4. The 9 in the ones place does not matter.
Rounding is the usual first step of an estimate: 4.87 × 9.2 ≈ 5 × 9 = 45.
Money is rounded to the nearest cent, the hundredths place: 12.346 dollars is about 12.35 dollars.
Some situations override the rule: you round up the number of buses needed and round down the number of items you can afford.

The rounding rule

digit to the right ≥ 5: round up; digit to the right ≤ 4: round down

rounding digit: the digit in the place you are rounding to
digit to the right: the one digit just after it; it alone decides up or down

Watch for carrying: 396 to the nearest ten is 400, because rounding the 9 tens up makes 10 tens. Keep a final 0 when it shows the place: 3.97 to the nearest tenth is 4.0.

Rounding examples, step by step

Example 1: Round to the nearest hundred

Warm-up

Round 6,482 to the nearest hundred.

The hundreds digit is 4 (6,482).
Look at the digit to its right, the tens digit: 8.
8 is 5 or more, so round up: 4 hundreds become 5 hundreds, and the digits after become 0.

Answer: 6,482 rounds to 6,500.

Example 2: Round a decimal

Core

Round 12.0745 to the nearest hundredth.

The hundredths digit is 7 (12.07|45).
The digit to its right is 4.
4 is less than 5, so round down: keep the 7 and drop the digits after it.
The later 5 does not matter; only the next digit counts.

Answer: 12.0745 rounds to 12.07.

Example 3: Rounding with carrying

Test-style

A stadium sold 39,962 tickets. Round this number to the nearest hundred.

The hundreds digit is 9 (39,962), and the digit to its right is 6, so round up.
9 hundreds plus 1 hundred is 10 hundreds, which is 1 thousand: carry 1 into the thousands place.
39 thousands become 40 thousands, and the hundreds, tens and ones become 0.

Answer: 39,962 rounds to 40,000 to the nearest hundred.

Common mistakes

✗ MistakeRounding 149 to the nearest hundred: 149 to 150, then 150 to 200.

✓ InsteadLook only at the tens digit, 4: round down to 100.

Look at the digit to the right of the place you are rounding to. Rounding in steps from the far right can give the wrong answer.

✗ MistakeRounding 73 to the nearest ten as 80, because 7 is 5 or more.

✓ InsteadThe digit to check is the ones digit, 3, so 73 rounds to 70.

The rounding digit itself never decides. The digit to its right does.

✗ MistakeRounding 2,683 to the nearest hundred as 27.

✓ Instead2,683 rounds to 2,700; the tens and ones places become zeros.

Rounding keeps the size of the number. Replace the dropped whole-number digits with 0, do not delete them.

✗ MistakeRounding 5.96 to the nearest tenth as 5.10.

✓ InsteadThe 9 tenths round up to 10 tenths, which is 1 more whole: 6.0.

When the rounding digit is 9 and rounds up, carry 1 into the next place to the left.

Not to be confused with

Roundingvs.Estimate

An estimate is any approximate answer to a calculation. Rounding is one way to make one: round the numbers, then compute, as in 48 × 21 ≈ 50 × 20.

Roundingvs.Truncating

Truncating just chops off digits without looking at them: 3.68 becomes 3.6. Rounding checks the next digit, so 3.68 becomes 3.7.

Roundingvs.Significant figures

Rounding to a place (nearest tenth) fixes where to stop. Rounding to significant figures counts digits from the first nonzero one: 0.004587 to 2 significant figures is 0.0046.

Quick check: 3 questions

Question 1 of 3

Round 7,350 to the nearest thousand.

Show answer and explanation

Answer: A. The thousands digit is 7 and the next digit is 3, so round down to 7,000. Choice B looks at the 5 instead of the 3, C rounds to the nearest hundred, and D just drops the last digits.

Question 2 of 3

Round 0.4567 to the nearest tenth.

Show answer and explanation

Answer: C. The tenths digit is 4 and the hundredths digit is 5, so round up to 0.5. Choice A truncates, B rounds to hundredths, and D rounds to thousandths.

Question 3 of 3

A whole number rounds to 60 when rounded to the nearest ten. Which could it be?

Show answer and explanation

Answer: D. Numbers from 55 to 64 round to 60. 55 is exactly halfway and rounds up to 60. 54 rounds to 50, and 65 and 66 round to 70.

Rounding: frequently asked questions

Does 5 round up or down?

In school math, 5 rounds up: 45 rounds to 50, and 2.35 rounds to 2.4 to the nearest tenth. A number exactly halfway has no closer neighbor, so the rule simply picks up. Some calculators and scientists use other tie rules, such as rounding to the even neighbor, but tests in US schools expect 5 to round up.

What does round to the nearest tenth mean?

It means keep one digit after the decimal point, choosing the closest value: 3.68 becomes 3.7 and 3.62 becomes 3.6. Look at the hundredths digit to decide. Nearest hundredth keeps two decimal places (12.346 becomes 12.35), and nearest whole number keeps none (7.5 becomes 8).

Why do we round numbers?

To make numbers easier to say, compare and compute with, when the exact value is not needed. Rounding lets you estimate 398 × 52 ≈ 400 × 50 = 20,000 in your head, report a city population as about 85,000, or give a price to the nearest cent. It also helps you check whether an exact answer is reasonable.

Practice and tools

Effortless Math practicePractice on Effortless Math Rounding CalculatorRound to any place value with the rule shown Significant Figures CalculatorRound to a number of significant figures

Sources

Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 3.NBT.A.1, CCSS 4.NBT.A.3, CCSS 5.NBT.A.4

Cite this entry

Effortless Math Team. “Rounding.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/rounding/

Flashcard

TermRounding5 or more, round up

DefinitionReplacing a number with a nearby simpler one at a chosen place. 684 to the nearest hundred is 700, because the tens digit is 8.

Study the full deck

Browse all terms in the Math Dictionary · More number system terms · Random term

NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2Decimal PointA decimal point is the dot that separates the whole-number part of a number from its fractional part. Digits to its left are ones, tens and hundreds; digits to its right are tenths, hundredths and thousandths. In 46.25 the point sits between 6 ones and 2 tenths, and you read it aloud as “and”.Number System · Grade 4, Grade 5, Grade 6Place ValuePlace value is the value of a digit based on its position in a number. In 3,507 the 5 is worth 500, because it sits in the hundreds place. Each place is worth 10 times the place to its right: ones, tens, hundreds, thousands, and after the decimal point, tenths and hundredths.Number System · Grade 3, Grade 4, Grade 5Number LineA number line is a straight line with numbers placed at equal distances along it, so every point stands for a number. Zero sits in the middle, positive numbers go to the right and negative numbers to the left. Numbers increase from left to right, so a number line shows order, distance and adding as moving.Number System · Grade 2, Grade 3, Grade 6EstimateAn estimate is an answer that is close to the exact one, and to estimate is to find an answer that is close enough, usually by rounding or using friendly numbers. For example, 49 × 21 is about 50 × 20 = 1000. Estimation helps you check whether an exact answer is reasonable.Problem Solving · Grade 3, Grade 4, Grade 5Rounded to the NearestRounded to the nearest tells you which place value to keep when you round an answer. Nearest tenth keeps one decimal place; nearest whole number keeps none. Look at the next digit to the right: 5 or more rounds up, 4 or less rounds down. So 3.14159 becomes 3.14 to the nearest hundredth.Problem Solving · Grade 3, Grade 4, Grade 5HundredthsHundredths are the parts you get when one whole is split into 100 equal parts; one hundredth is 1100 or 0.01. The hundredths place is the second digit to the right of the decimal point, so in 3.47 the 7 means 7 hundredths. One cent is one hundredth of a dollar.Number System · Grade 4, Grade 5, Grade 6TenthsTenths are the parts you get when one whole is split into 10 equal parts; each part is one tenth, written 110 or 0.1. The tenths place is the first digit to the right of the decimal point, so in 4.7 the 7 means 7 tenths, or 0.7.Number System · Grade 3, Grade 4, Grade 5Whole NumberA whole number is 0 or a positive counting number: 0, 1, 2, 3, and so on. Whole numbers do not include fractions, decimals, or negative numbers, so 12 is a whole number but 8.5, 34 and −3 are not. Every whole number is also an integer.Number System · Grade 3, Grade 4, Grade 5PopulationA population in statistics is the whole group of people, animals or objects you want to learn about, such as every student in a school or every bulb a factory makes. Measuring all of them is often too costly, so you study a sample, a part of the population, and use it to draw conclusions about the whole group.Statistics · Grade 7, Statistics, Algebra 1DecimalA decimal is a number written with a decimal point to show parts of a whole. Decimals use place value to represent tenths, hundredths, thousandths and more: in 3.14, the 1 means 1 tenth and the 4 means 4 hundredths. So 0.75 = 75100, and 0.5 is one half.Number System · Grade 4, Grade 5, Grade 6DigitA digit is one of the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 that we use to write every number. The number 507 has three digits: 5, 0 and 7. What a digit is worth depends on its place: in 507, the 5 stands for 5 hundreds, or 500.Number System · Grade 1, Grade 2, Grade 3Scientific NotationScientific notation writes a number as a value from 1 to less than 10 times a power of 10, such as 5.4 × 10³ for 5,400. The exponent records how far the decimal point moved: positive for large numbers and negative for numbers between 0 and 1, as in 0.0062 = 6.2 × 10⁻³.Number System · Grade 8, Algebra 1PercentA percent is a number out of 100. Percent means per hundred, so 25% means 25 out of 100, or 25100 = 0.25. To find a percent of a quantity, change the percent to a decimal and multiply: 20% of 80 is 0.20 × 80 = 16. The symbol for percent is %.Number System · Grade 5, Grade 6, Grade 7MeanThe mean is the sum of the values divided by the number of values. It is the arithmetic average: add every value and divide by how many there are. For 3, 7, 5 and 9, the mean is 24 ÷ 4 = 6. The mean is the balance point of the data, so one outlier can pull it far.Statistics · Grade 5, Grade 6, Grade 7ReasonablenessReasonableness is checking whether an answer makes sense for the problem before you accept it. Estimate first to see about how big the answer should be, then check the units and the context: a negative length, 3.5 people or 800 dollars for one pencil is not reasonable. A correctly calculated number can still fail this check.Problem Solving · Grade 3, Grade 4, Grade 5

Rounding

What is rounding in math?

Rounding in a picture

Formal definition and notation

Key facts

The rounding rule

Rounding examples, step by step

Example 1: Round to the nearest hundred

Example 2: Round a decimal

Example 3: Rounding with carrying

Common mistakes

Not to be confused with

Quick check: 3 questions

Rounding: frequently asked questions

Does 5 round up or down?

What does round to the nearest tenth mean?

Why do we round numbers?

Related terms

Practice and tools

Sources

Flashcard

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