What is rounding?
Rounding replaces a number with a simpler one that is close to it, when the exact value isn't needed. A number is rounded to a place value, like the nearest ten or the nearest hundredth, depending on how precise it has to be: a gas price of $3.279 a gallon is paid as $3.28, to the nearest cent.
Source OpenStax Prealgebra 2e · 1.1: Round whole numbers (HOW TO round a whole number to a place value) ↗OpenStax Prealgebra 2e · 5.1: Round decimals (HOW TO round a decimal) ↗
How to round numbers
Here it is with your numbers:
- Find the hundredths digit: 18.379.
- Look at what comes after it: the digit 9.
- The next digit, 9, is 5 or more, so the hundredths digit goes up.
- Drop the digits after the hundredths: 18.38.
It means 18.379 is 18.38 to the nearest hundredth.
A 9 that goes up carries: 9.995 to the nearest hundredth is 10.00. Rounded decimals keep their places, so 2.996 becomes 3.00, not 3.
Your number rounded to each place
| Rounded to the | Answer |
|---|---|
| Nearest ten | 20 |
| Nearest whole number | 18 |
| Nearest tenth | 18.4 |
| Nearest hundredth | 18.38 |
| Nearest thousandth | 18.379 |
Rounding methods: halves, ceiling and floor
The ten ways to round only differ for halves and negative numbers. The first six go to the nearer choice; the last four always go one way:
| How to round | 2.5 | −2.5 | 2.4 | −2.4 |
|---|---|---|---|---|
| Nearest, halves away from zero (usual) | 3 | −3 | 2 | −2 |
| Nearest, halves to even (banker’s) | 2 | −2 | 2 | −2 |
| Nearest, halves to odd | 3 | −3 | 2 | −2 |
| Nearest, halves up (towards +∞) | 3 | −2 | 2 | −2 |
| Nearest, halves down (towards −∞) | 2 | −3 | 2 | −2 |
| Nearest, halves towards zero | 2 | −2 | 2 | −2 |
| Up (ceiling, towards +∞) | 3 | −2 | 3 | −2 |
| Down (floor, towards −∞) | 2 | −3 | 2 | −3 |
| Away from zero (ROUNDUP) | 3 | −3 | 3 | −3 |
| Towards zero (ROUNDDOWN) | 2 | −2 | 2 | −2 |
Spreadsheets round halves away from zero, and their ROUNDUP and ROUNDDOWN go away from and towards zero: ROUNDUP(−3.14159, 1) is −3.2, while the ceiling is −3.1. JavaScript’s Math.round takes halves up the number line.
Source NIST GLP 9 (2019) · Rounding: even/odd and spreadsheet rounding ↗General Decimal Arithmetic Specification · The arithmetic model: rounding (half-down, ceiling, floor, up, down) ↗ECMAScript Language Specification · Math.round (halves towards +∞) ↗Microsoft Support · ROUND function ↗Microsoft Support · ROUNDUP function ↗Microsoft Support · ROUNDDOWN function ↗
Rounding examples
FAQs
What is the rule for rounding numbers?
Look at the digit just to the right of the place you are rounding to. If it is 5 or more, add 1 to the place digit; if it is less than 5, leave it. Then drop the digits after it, or replace them with zeros in a whole number. 18.379 to the nearest hundredth is 18.38.
Source OpenStax Prealgebra 2e · 5.1: Round decimals (HOW TO round a decimal) ↗
Is 2.5 rounded to 2 or 3?
With the usual rule, 2.5 rounds up to 3, because the digit after the ones place is 5. With banker’s rounding (halves to even) it rounds to 2, the even choice, while 3.5 rounds to 4.
Source NIST GLP 9 (2019) · Rounding: even/odd and spreadsheet rounding ↗
Is 7 rounded to 5 or 10?
To the nearest ten, 7 rounds to 10: the ones digit, 7, is 5 or more, so the tens digit goes up from 0 to 1. Rounding to the nearest ten always gives a multiple of 10, never 5.
Source OpenStax Prealgebra 2e · 1.1: Round whole numbers (HOW TO round a whole number to a place value) ↗
What is the difference between banker’s rounding and standard rounding?
They only differ when the part dropped is exactly half: standard rounding takes 2.5 up to 3, banker’s rounding takes it to the even digit, 2. NIST prefers it for statistics, because always rounding halves up pushes averages up.
Source NIST GLP 9 (2019) · Rounding: even/odd and spreadsheet rounding ↗
How do I round up numbers?
To round up whatever the digits after the place are, add 1 to the place digit if anything other than zeros comes after it: 3.14159 rounded up to three decimal places is 3.142. In Excel or Google Sheets, =ROUNDUP(3.14159, 3) does the same. Choose “Away from zero” above.
Sources
- OpenStax Prealgebra 2e: 1.1: Round whole numbers (HOW TO round a whole number to a place value)
- OpenStax Prealgebra 2e: 5.1: Round decimals (HOW TO round a decimal)
- NIST GLP 9 (2019): Rounding: even/odd and spreadsheet rounding
- General Decimal Arithmetic Specification: The arithmetic model: rounding (half-down, ceiling, floor, up, down)
- ECMAScript Language Specification: Math.round (halves towards +∞)
- Microsoft Support: ROUND function
- Microsoft Support: ROUNDUP function
- Microsoft Support: ROUNDDOWN function