Rounding

Definition

Rounding Numbers means adjusting the digits of a number in such a way that it gives an approximate value. This value is an easier representation of the given number. For example, the population of a town could be easily expressed as 700,000 rather than 698,869. Rounding numbers makes calculations simpler, resulting in a figure that is easy to remember. However, rounding of numbers is done only for those numbers where the exact value does not hold that much importance.¹

Who

Simply put, rounding numbers simply allows you to look at numbers in an easier and simpler way. The truth is that when you round numbers, they will seem less accurate. And there’s a point of truth here. Nevertheless, in most instances, this won’t make any difference at all.

The truth is that many people keep rounding numbers in their daily lives and they don’t even notice that they are doing so. For example, when you are about to make a purchase, it’ normal that you round numbers. It’s not unusual at all to see prices such as $1.98, $53.95, $89.99. But when you are interested in buying these items, you instantly see their prices in a rounded form. You don’t do the math in your mind and add exactly $1.98 + $53.95 + $89.99. Instead, what you do is that you round the numbers to make the addition easier. So, in your mind, you add the rounded numbers:

$2 + $54 + $90

In some cases, you may even do it this way:

$2 + $55 + $90

And if you check the results, there isn’t much difference between them.

But rounding numbers isn’t simply a strategy that you apply to when you want to make a purchase. Another example where you usually round numbers is to know how much time you take to get from home to work. Let’s say that you usually take 25 minutes. When you are talking to someone about the time you take from home to work, then you probably tell them that it takes you half an hour to get there or 30 minutes.

Another simple example when you round numbers and you don’t even realize it is when you look at the population of one city. Let’s take New York City as an example. You probably know that New York City has about 8 million people. However, you know that this isn’t the exact number. It’s an approximate number, it’s a rounded number that allows you to easily memorize. In case you don’t know, New York City has 8,214,426 people.⁵

What

Rounding decimals consists of rounding a decimal number to a certain number of decimal places, to save time and help us express really long numbers in shorter terms. We can round decimals to the nearest wholes, tenths or hundredths, when having exact values isn’t important. A rounded number has almost the same value as the original number but it is a bit less exact.²

Why

When dealing with decimal numbers, rounding is an important concept that everyone should master. Rounding is useful in different situations: rounding to pay bills or in an academic setting to find out the estimate of the average score of students in a class.²

See Theoretical Knowledge Vs Practical Application.

How

There are certain rules to follow when rounding a decimal number. Put simply, if the last digit is less than 5, round the previous digit down. However, if it’s 5 or more than you should round the previous digit up. So, if the number you are about to round is followed by 5, 6, 7, 8, 9 round the number up. And if it is followed by 0, 1, 2, 3, 4 round the number down.²

A decimal number is a combination of a whole number part and a fractional part separated by a decimal point. Rounding decimal numbers works in the same way as we round whole numbers although we need to know the decimal place values of all the digits in the given number. This refers to the digits given before the decimal point as well as the digits given after the decimal point. Observe the decimal place value chart to understand this better.¹

Rounding a Number in Microsoft Excel

In some situations when you don’t need an exact answer, rounding is a useful skill to use. In plain English, to round a number is to eliminate the least significant digits, making it simpler but keeping close to the original value. In other words, rounding lets you get an approximate number with the desired level of accuracy.

In everyday life, rounding is commonly used to make numbers easier to estimate, communicate or work with. For instance, you can use rounding to make long decimal numbers shorter to report the results of complex calculations or round off currency values.

Many different ways of rounding exist, such as rounding to integer, rounding to a specified increment, rounding to simple fractions, and so on. And Microsoft Excel provides a handful of functions to handle different rounding types.⁴

Excel provides a number of rounding functions, each with a different behavior:³

To round with standard rules, use the ROUND function.
To round to the nearest multiple, use the MROUND function.
To round down to the nearest specified place, use the ROUNDDOWN function.
To round down to the nearest specified multiple, use the FLOOR function.
To round up to the nearest specified place, use the ROUNDUP function.
To round up to the nearest specified multiple, use the CEILING function.
To round down and return an integer only, use the INT function.
To truncate decimal places, use the TRUNC function.

Many of the References and Additional Reading websites and Videos will assist you with rounding numbers.

As some professors say: “It is intuitively obvious to even the most casual observer.“

References

¹ “Rounding Numbers – Rules, Examples For Rounding Numbers”. 2022. cuemath. https://www.cuemath.com/numbers/rounding-numbers/.

2 “How To Round Decimals ? | Rounding Numbers Guide”. 2021. Blogue Tutorax. https://tutorax.com/blogue/en/how-to-round-decimals-rounding-numbers-guide/.

³ “How To Use The Excel ROUND Function | Exceljet”. 2022. exceljet.net. https://exceljet.net/excel-functions/excel-round-function.

⁴ Cheusheva, Svetlana. 2021. “Rounding In Excel: ROUND, ROUNDUP, ROUNDDOWN, FLOOR, CEILING Functions – Ablebits.com”. Ablebits.com. https://www.ablebits.com/office-addins-blog/2015/08/06/excel-round-functions/.

⁵ “Why Do You Need To Know How To Round Numbers – Rounding.To”. 2020. Rounding.To. https://rounding.to/why-do-you-need-to-know-how-to-round-numbers/.

Additional Reading

“10, 50, 100: Why Do We Find Comfort In Round Numbers? – WHYY”. 2022. WHYY. https://whyy.org/segments/10-50-100-why-do-we-find-comfort-in-round-numbers/.

“Rounding Calculator – rounding.to”. 2022. rounding.to. https://rounding.to/.

“Rounding Methods”. 2022. mathsisfun.com. https://www.mathsisfun.com/numbers/rounding-methods.html.

“Rounding Numbers”. 2022. mathsisfun.com. https://www.mathsisfun.com/rounding-numbers.html.

“Rounding Numbers Calculator”. CalculatorSoup, LLC. 2022. https://www.calculatorsoup.com/calculators/math/roundingnumbers.php.

“What Is Rounding Decimals? – Definition Facts And Examples”. 2022. SplashLearn – Math Vocabulary. https://www.splashlearn.com/math-vocabulary/decimals/rounding-decimals.

Videos

Estimating adding large numbers by rounding

Rounding to the nearest 10 on the number line

“Addition, Subtraction, And Estimation | 3Rd Grade | Math | Khan Academy”. 2022. Khan Academy. https://www.khanacademy.org/math/cc-third-grade-math/imp-addition-and-subtraction#imp-rounding.

Rounding Numbers and Rounding Decimals – The Easy Way!

This math video tutorial provides a basic introduction into rounding. It explains the process of rounding numbers and rounding decimals.