Round to the Nearest Whole Number
Rounding to the nearest whole number means converting a number to an approximate value that is easier to use and remember. Usually, decimal numbers and fractions are rounded to the nearest whole number with the help of the appropriate rules. Let us learn how to round to the nearest whole number in this article.
| 1. | What is Rounding to the Nearest Whole Number? |
| 2. | Rules for Rounding to the Nearest Whole Number |
| 3. | Rounding Decimals to the Nearest Whole Number |
| 4. | FAQs on Round to the Nearest Whole Number |
What is Rounding to the Nearest Whole Number?
In order to round a decimal or fraction to the nearest whole number, we need to follow a certain set of rules. Rounding to the nearest whole number converts the number to such a figure which is easier to remember and use. For example, a distance of 6.87 miles can be expressed as 7 miles approximately, which is a whole number. Similarly, expressing the quantity of oil as 8 liters is easier rather than writing it as \(7 \dfrac{4}{5}\) liters. However, it should be noted that rounding of numbers is done in those cases where the exact value is not needed and the approximate value can be used.
To round decimal numbers to the nearest whole number, we always check the tenths digit, which is the digit to the immediate right of the decimal point. If this digit is equal to or more than 5, then the given number is rounded up, and if it is less than 5 then the given number is rounded down. The term 'rounding up' is used when the number increases after rounding, while 'rounding down' is used when the number decreases after rounding. For example, when 6.87 is rounded to 7, it is rounded up; and when 6.34 is rounded to 6 it is said to be rounded down.
Example 1: Round 2.8 to the nearest whole number.
Solution: Since we need to round the given decimal to the nearest whole number, we will check the tenths digit. In this case, the tenths digit is 8, which is more than 5. So, the number will be rounded up to 3. In other words, 2.8 ≈ 3
This can also be understood with the help of a number line. We know that 2.8 lies between 2 and 3. So, if we draw a number line as shown below, we can see that 2.5 lies midway between 2 and 3, and 2.8 is closer to 3 rather than 2. Therefore, 2.8 will be rounded to 3.
Rules for Rounding to the Nearest Whole Number
There are two basic rules to round a decimal to the nearest whole number.
- If the digit on the tenths place is less than 5, the rounding digit (the digit on ones place) remains the same and all the following digits including the decimal point are removed.
- If the digit on the tenths place is 5 or more than 5, we increase the rounding digit (the digit on ones place) by 1, and all the following digits including the decimal point are removed.
When fractions are rounded to the nearest whole number, we follow a simple rule of comparing the proper fraction to 1/2.
- If the given fraction is an improper fraction, we need to change it to a mixed fraction and then compare the fractional part with 1/2. We round up the fraction if it is equal to or greater than 1/2, and we round down if it is less than 1/2.
Rounding Decimals to the Nearest Whole Number
Rounding decimals to the nearest whole number converts it into an easier number. Let us understand this with an example using the rules given above.
Example 1: Round 26.45 to the nearest whole number.
Solution:
We will check the digit on the tenths place which is 4 in this case. Since 4 is less than 5, we will round down the number to 26 and remove the following digits including the decimal point. Therefore, the rounded whole number is 26.
Now, let us see how to round a decimal to a whole number if the digit on the tenths place is more than 5. In this case, we round up the given decimal.
Example 2: Round 26.85 to the nearest whole number.
Solution: We will check the digit on the tenths place which is 8 in this case. Since 8 is more than 5, we will round up the number to 27 and remove the following digits including the decimal point. Hence, the rounded whole number is 27.
Rounding Fractions to the Nearest Whole Number
Rounding fractions to the nearest whole number follows a simple rule of comparing the proper fraction to 1/2. In the case of a mixed fraction, the whole number part is kept aside, and the fractional part is compared with 1/2. If this fraction is less than 1/2, the given fraction is rounded down and if it is more than 1/2, it is rounded up.
Example: Round the following fractions to the nearest whole number.
a.) 4/5
b.) \(15 \dfrac{2}{5}\)
c.) 36/5
Solution:
a.) First, we will compare 4/5 with 1/2. Since these are unlike fractions, we will find the Least Common Multiple (LCM) and then compare them. This will make it 8/10 and 5/10 respectively. After this step, we get to know that 4/5 is greater than 1/2, so, it will be rounded off to 1.
b.) \(15 \dfrac{2}{5}\) is a mixed fraction. For rounding mixed fractions to the nearest whole number, we keep the whole number part aside and only compare the fractional part with 1/2. So, keeping 15 aside, we will check if 2/5 is greater than or less than 1/2. Since 2/5 is less than 1/2, we will round the given mixed fraction to 15.
c.) 36/5 is an improper fraction, so we will convert it to a mixed fraction which will make it \(7 \dfrac{1}{5}\). Now, keeping the whole number part aside, we will compare the fractional part with 1/2. Therefore, keeping 7 aside, we will check if 1/5 is greater than or less than 1/2. Since 1/5 is less than 1/2, we will round the given fraction to 7.
Note: Another way to round fractions to the nearest whole number is by changing the given fractions to their decimal form and then rounding them using the given rules of decimals. For example, 12/5 can be written as 2.4 in the decimal form. Now, if we check the tenths place in 2.4, it is 4, which is less than 5. So, it will be rounded to 2.
Related Links
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FAQs on Round to the Nearest Whole Number
What does Round to the Nearest Whole Number mean?
Rounding to the nearest whole number means converting a decimal or a fraction to an approximate whole number whose value is close to it. Rounding to the nearest whole number makes it easier to remember the figure and makes calculation simpler. For example, 2.6 is rounded to a whole number and is expressed as 3, similarly, \(2 \dfrac{1}{4}\) can be rounded off to 2.
How to Round to the Nearest Whole Number with Decimals?
In case of rounding decimals to the nearest whole number, the digit on the tenths place is checked. This is the digit to the immediate right of the decimal point. If this digit is less than 5, then the ones digit remains as it is, and the following numbers along with the decimal are removed. If the digit on the tenths place is 5 or more than 5, then the given number increases by 1, and the remaining digits are removed including the decimal point. For example, to round 3.64 to the nearest whole number, we will check the digit on the tenths place, which is 6 in this case. Since it is more than 5, the given number will be rounded to 4.
What is Rounding up to the Nearest Whole Number?
While rounding is generic term, we use the terms 'rounding up' and 'rounding down' to distinguish when a number increases or decreases after rounding. If the number is rounded to the nearest whole number and it increases in value it is said to be rounded up. For example, when 3.62 is rounded to the whole number 4, it is said to be rounded up. Similarly, when 3.26 is rounded to 3, it is said to be rounded down.
Which Decimals Round to 15 when Rounding to the Nearest Whole Number?
When rounding to the nearest whole number, all the decimal numbers that have 14 as their whole number part and have 5 or more than 5 in their tenths digit are rounded to 15. For example, 14.5, 14.6, 14.7, 14.8, and 14. 9 round up to 15. Or, if the decimal number has 15 as the whole number part and the tenths digit is less than 5, then these decimals are also rounded to 15. For example, 15.1, 15.2, 15.3, and 15.4 round down to 15. Therefore, the numbers 14.5, 14.6, 14.7, 14.8, 14.9, 15.1, 15.2, 15.3, and 15.4 round to 15 when rounded to the nearest whole number.
Give an Example of Rounding to the Nearest Whole Number.
An example of rounding to the nearest whole number can be seen as follows. When 12.45 is rounded to the nearest whole number, it becomes 12 because the digit in the tenths place is less than 5. Similarly, when 12.73 is rounded to the nearest whole number, it becomes 13 because the digit on the tenths place is more than 5.
Round 13.45 to the Nearest Whole Number.
When 13.45 is rounded to the nearest whole number, it becomes 13 since the digit on the tenths place is 4 which is less than 5.
How to Round Mixed Numbers to the Nearest Whole Number?
Mixed numbers are also known as mixed fractions which consist of a whole number and a proper fraction. In order to round mixed numbers to the nearest whole number, we keep the whole number part aside and compare the proper fraction with 1/2. If the fraction is less than 1/2, then the given fraction is rounded down and if the fractional part is equal to or more than 1/2, then it is rounded up. For example, let us round \(7 \dfrac{1}{4}\) to the nearest whole number. Here, we will keep the whole number part (7), aside and compare the fractional part (1/4) with 1/2. After keeping 7 aside, when we compare 1/4 with 1/2, we get to know that 1/4 is less than 1/2. Therefore, the given fraction will be rounded down to 7.
Round 6.07 to the Nearest Whole Number.
When 6.07 is rounded to the nearest whole number, it becomes 6 since the digit on the tenths place is 0 which is less than 5.