Rounding off Numbers: Rules, Calculator and Examples

Rounding Numbers is the process of altering the digits of a number to deliver an approximate value. Round off Rules is easy to understand. For example, if a place’s population is 499,897, the round-off number will be 500,000.

Many quantitative values, such as the money, the distance travelled, the length measured, etc., are calculated by rounding the actual figure to the next whole number. This article will discuss the round off numbers definition, rules, and examples.

Rounding off Numbers

Definition: The rounding off number is more straightforward by keeping its value intact but closer to the following number. This is used for the whole numbers and the decimals at various places of hundreds, tens, tenths, etc. The number of essential figures resulting is simply the number of known figures with some reliability.

Example: You can see the number \(541\) is rounded off to the nearest hundred  \(500\) because \(541\) is much closer to \(500\) than \(600\). You can round off the number to the nearest tens, hundreds, thousands etc. 

Rules for Rounding off Numbers

For rounding off any number, there are a certain set of rules that should be followed. 

Rounding off to Nearest Tens

1. If the digit in one place is less than \(5\), then make the digit in one place zero and keep the digits the same in tens and higher place values.
2. If the digit in one place is equal to or more than \(5\), then make the number zero and increase the digits in tens place by \(1\).

Example: Rounding off \(76\), as you have \(6>5\), you round up, and the answer is \(80\).
Rounding off \(83\), as you have \(3<5\), you round down, and the answer is \(80\).

Rounding off to Nearest Hundreds

1. If you find the tens place digit less than \(5\), then make the digit in tens and ones place zero and keep the digits the same in hundreds and higher place values.
2. If the digit in tens place is equal to or more than \(5\), then make the digits in tens and ones place as zero, increase the digits in hundreds of place by \(1\), and keep the digits the same in higher place value.

Example: Rounding off \(267\), you see the digit in tens place is \(6>5\), so you round up, and the answer is \(300\).

Rounding off \(643\), you see the digit in tens place is \(4<5\), so you round down, and the answer is \(600\).

Rounding off to Nearest Thousands

1. If the digit in hundreds place is less than \(5\), then make the digits in hundreds, tens, and ones place zero and keep the digits the same in thousands and higher place values.
2.  If the digit in hundreds place is equal to or more than \(5\), then make the digits in hundreds, tens and ones place as zero and increase the digit in thousands place by \(1\) and keep the digits the same in higher place values than thousands.

Example: Rounding off \(8572\), you can see that digit in hundreds place \(5=5\), so you round up, and the answer is \(9000\).

Rounding off \(3218\), you can see that digit in hundreds place \(2<5\), so you round down, and the answer is \(3000\).

Rounding off Rules for Whole Numbers

Below are the given rules for rounding off the whole numbers:

1. You can choose a smaller number to get the accurate final result.
2. Now, look for the next smaller place towards the right of the number rounded off to. For example, if you want to round off a digit from a hundred places, look for a digit in the tens place.
3. If the digit in the minor place is less than \(5\), then the digit is left as it is. No matter how many digits you have after that number, it becomes zero, known as rounding down.
4. If the digit in the minor place is equal to or greater than \(5\), then you must add \(+1\) to that particular digit. The digit after that number will be turned to zero, which is known as rounding up.

Rounding off Fractions

You are aware that fractions are written in \(\left( {\frac{p}{q}} \right)\), where \(q\) not equal to zero. Follow the given steps to round off the fractions:

1. You should have whole numbers in the numerator and denominator placesIf you don’t have a whole number, you have to follow the decimal point shifting rule of fractions to make them real numbers. 
2. Now, you take the numerator and the denominator separately.
3. Here, they both are rounded off separately, using the rules for rounding off numbers.
4. Not having an equal number of zeros from the numerator and the denominator can be ignored after rounding off.
5. Finally, you round off the fraction.

Example: You have the fraction as \(\frac{{231}}{{170}}\). Since \(1\) is smaller than \(5\), round off the number \(231\) to \(230\). 

Now, rounding off the number \(170\) to its nearest tens will be the same as \(170\) only. 

Here, you get the rounded off fraction as \(\frac{{230}}{{170}}\). So, by dropping the trailing zeros from both the numerator and the denominator, you get \(\frac{{23}}{{17}}\). Hence, the rounded fraction is \(\frac{{23}}{{17}}\).

Rounding off Decimals

There are specific rules to follow for rounding off the decimal number, and they are given below:

1. Identify the rounding off digit and then look at its righthand side.
2. If the digit at the righthand side is less than \(5\), consider it as equal to zero.
3. If the digit at the righthand side is greater than or equal to \(5\), add \(+1\) to the digit and write all the other digits as zero.

Example: \(5.1837\) round off to the nearest hundredth, and that would be \(5.18\) as you rounding down since \(3<5\).

But, to the nearest thousandth, it is \(5.184\) as you rounded up because \(7>5\).

Estimation of the Sum or Difference

While estimating the numbers during addition or subtraction, you should know the place up to which the numbers can be rounded off. 

Example: Estimating the sum of \(29043\) and \(6751\), we see that \(29043>6751\). So, both the numbers can be rounded off to the nearest thousands as \(29000\) and \(7000\).

Hence, \(29000+7000=36000\)

Solved Examples

Q.1. Round off the number to the nearest tens: \(652\).
Ans: We need to round off \(652\) to the nearest ten.
In the number \(652\), the digit in the one’s place is less than \(5\), so we shall round down.
Hence, rounding off \(652\) to the nearest ten gives \(650\).

Q.2. Round off the number to the nearest hundreds: \(787\).
Ans: We need to round off \(787\) to the nearest hundred.
In the number \(787\), the digit in the tens place is more than \(5\), so we shall round up.
Hence, rounding off \(787\) to the nearest hundreds gives \(800\).

Q.3. Round off the number to the nearest thousands: \(7890\).
Ans: We need to round off \(7890\) to the nearest thousand.
In the number \(7890\), the digit in the hundreds place is more than \(5\), so we shall round up.
Hence, rounding off \(7890\) to the nearest thousands gives \(8000\).

Q.4. Round off the decimal \(3.7\) into whole number.
Ans: Given, \(3.7\)
\(3.7=4\)  (we have rounded off to the nearest whole number).

Q.5. Round off the given fraction: \(\frac{{562}}{{987}}\) to nearest tens.
Ans: Here, we shall round off the numerator and denominator separately correct to tens place.
So, \(562\) rounded to tens place is \(560\) and \(987\) rounded to tens place is \(990\).
Hence, the fraction \(\frac{{562}}{{987}}\) correct to the nearest tens place is \(\frac{{560}}{{990}} = \frac{{56}}{{99}}\).

Summary

In this above article, you have gone through the term rounding off the numbers. Then, we have also covered some of the rules of rounding, the how-to round off the whole numbers, fractions and decimals. Finally, we glanced at types of rounding off numbers like rounding off the number to its tens, hundreds, thousand etc., covered some of the solved examples and a few FAQs.

FAQs

Q.1. How do you round off when there’s \(5\)?
Ans: When any number has \(5\), we moved forward because you round off to the next nearest tens or hundreds or thousands when the digit is \(5\) or more than \(5\).
Example: \(65\) is a number, so we round off to \(70\).

Q.2. What is meant by rounding off a number?
Ans: Rounding off the numbers defines adjusting the digits to their nearest tens, hundreds, thousands and so on to make rough calculations more accessible, and the answer which you get will be an estimated answer rather than the precise one.

Q.3. What are the rules of rounding off?
Ans: The general rule of the rounding off numbers is if the digit you want to round off is followed by \(0, 1, 2, 3, 4\), then you go backwards, and if the digit is followed by \(5, 6, 7, 8, 9\) then you move forward.

Q.4. How do you round off hundreds?
Ans: When you want to round off the nearest hundreds, you have to check the digit in the tens place. If the digit is equal to or more than the digit \(5\), then you round off to the previous hundred, and if the digit is more than \(5\) or \(5\) you round off to the next hundreds.
Example: \(425\) in this number, the digit in tens place is \(2\), which is less than \(5\), so round off to the previous hundred that is \(400\).
\(879\) in this number, the digit in tens place is \(7\), which is more than \(5\), so round off to the next hundred that is \(900\).

Q.5. How do you round off?
Ans: When you want to round off any number, check the digit you want to round off is less than \(5\) or \(5\) or more than \(5\). If it is less than \(5\) you move to the previous tens or hundreds or thousands. If it is \(5\) or more than \(5\) you move forward.
Example: \(78=80\) as \(8\) is more than \(5; 734=700\) as \(34\) is less than \(50\).

We hope this detailed article on round off numbers proves helpful to you. If you have any doubts or queries, comment down below and we will be ready to help you at the earliest.