This entry was posted on April 24, 2022 by Anne Helmenstine (updated on June 6, 2022)
Rounding numbers gives your numbers that are close in value to the starting numbers, but are less exact. For example, rounding 241 to the nearest ten gives you 240. Rounding 243 to the nearest ten also is 240, while 246 rounds to 250. Here are the rules for rounding numbers and sums. Also, learn about rounding in significant figures.
Rules for Rounding Numbers
It may surprise you that there are lots of different ways of rounding numbers. Each method has its own rules, advantages, and disadvantages. However, the most common method rounds up when the digit in question is followed by a 5 or higher:
- Round up if the digit you are rounding is followed by a 5, 6, 7, 8, or 9. For example, 48 rounded to the nearest ten is 50.
- Round down if the digit you are rounding is followed by a 0, 1, 2, 3, or 4. For example, 23 rounded to the nearest 10 is 20.
Here is a rhyme to help you remember:
Find your place,
look next door.
5 or greater, add one more.
Finding Your Place
First, decide what place you are rounding to, whether it’s the nearest, tenth, one, ten, hundred, thousand, and so on. Here are some examples:
- 3947 rounded to the nearest ten is 3950
- 3947 rounded to the nearest hundred is 3900
- 3947 rounded to the nearest thousand is 4000
Note that all of the digits to the right of the place you are rounding become zeros. Rounding decimals works the same way. For example:
<!-MONUMETRIC Repeatable 2 D:300x250 T:300x250 M:300x250,320x50 START->
<!-MONUMETRIC Repeatable 2 D:300x250 T:300x250 M:300x250,320x50 ENDS->
- 21.0538 rounded to the nearest one is 21
- 21.0538 rounded to the nearest tenth is 21.1
- 21.0538 rounded to the nearest hundredth is 21.05
- 21.0538 rounded to the nearest thousandth is 21.054
Note you do not add zeros to the right of the decimal point.
Rounding Numbers Worksheets
Practice rounding numbers with these worksheets, available as PDF, Google Apps, or PNG files to download or print.
Round Numbers to the Nearest 10
[worksheet PDF][worksheet Google Apps][worksheet PNG][answers PNG]
Round Numbers to the Nearest 100
[worksheet PDF][worksheet Google Apps][worksheet PNG][answers PNG]
Round Numbers to the Nearest 1000
[worksheet PDF][worksheet Google Apps][worksheet PNG][answers PNG]
Round Numbers to the Nearest Tenth
[worksheet PDF][worksheet Google Apps][worksheet PNG][answers PNG]
Round Numbers to Nearest Hundredth
[worksheet PDF][worksheet Google Apps][worksheet PNG][answers PNG]
Round Numbers to Nearest Thousandth
[worksheet PDF][worksheet Google Apps][worksheet PNG][answers PNG]
Rounds Sums – Money
Monetary sums typically go to the hundredth place (depending on your country). Rounding sums makes estimating the cost of items a lot easier than walking around with a calculator.
For example, if you want to know how much three items cost:
- $2.25
- $2.68
- $0.88
Rounding the numbers makes the math simple:
- $2.00
- $3.00
- $1.00
Adding 2 + 3 + 1 in your head gives you a total of 6. So, you know the items cost close to $6.00 (actual cost is $5.81). If the items are taxable, an easy way of getting close to the final value is always rounding up!
Rules for Rounding Negative Numbers
Rules for rounding negative numbers differ between disciplines. Here are some common methods:
- Round half away from zero: For example, 23.5 rounds to 24 and -23.5 rounds to -24. This method is common in sciences, commercially, and with binary computers because it is simple and deals with positive and negative numbers symmetrically.
- Round half toward zero: For example, 23.5 rounds to 23 and -23.5 rounds to -23.
- Round half up (toward positive infinity): For example, 23.5 rounds to 24 and -23.5 rounds to -23.
- Round half down (toward negative infinity): For example, 23.5 rounds to 23 and -23.5 rounds to -24.
- Round half to even: For example, 23.5 and 24.5 round to 24 and -23.5 -24.5 round to -24.
- Round half to odd: Here, 22.5 and 23.5 round to 23, while 24.5 rounds to 25. Both -22.5 and -23.5 round to -23, while -24.5 rounds to -25.
Rules for Rounding Significant Figures
Scientists, engineers, and other professionals who perform measurements report final values using significant figures.
- If the first non-significant digit is less than 5, the least significant digit remains the same.
- If the first non-significant digit is greater than 5, increase the least significant digit by 1.
- However, if the first non-significant digit is 5, the least significant digit either remains unchanged or increases by 1. Rounding off introduces error, so one common method of offsetting it is increasing the least significant digit by 1 if it is odd and leaving it unchanged if it is even.
When you perform calculations that involve multiple steps, it’s generally best to avoid rounding until you get the final answer.
References
- Borman, Phil; Chatfield, Marion (2015). “Avoid the perils of using rounded data”. Journal of Pharmaceutical and Biomedical Analysis. 115: 506–507. doi:10.1016/j.jpba.2015.07.021
- Higham, Nicholas John (2002). Accuracy and Stability of Numerical Algorithms. ISBN 978-0-89871-521-7.
- Kulisch, Ulrich W. (1977). “Mathematical foundation of computer arithmetic”. IEEE Transactions on Computers. C-26 (7): 610–621. doi:10.1109/TC.1977.1674893
- Lankham, Isaiah; Nachtergaele, Bruno; Schilling, Anne (2016). Linear Algebra as an Introduction to Abstract Mathematics. World Scientific. ISBN 978-981-4730-35-8.
