Rounding Numbers

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.

Let us learn more about rounding numbers, to get a better idea of how to round off a number to the nearest ten, hundred, thousand, and so on.

1.	What is Rounding Numbers?
2.	Rules for Rounding Numbers
3.	How to Round Off Whole Numbers?
4.	How to Round Off Fractions?
5.	How to Round Off Decimal Numbers?
6.	FAQs on Rounding Numbers

Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.

Let us understand the concept of rounding through an example. Susan covered a distance of 2.05 miles, which she noted as approximately 2 miles. How did she estimate the approximate value of the distance she covered? Why didn't she record her distance as 3 miles? Noting an approximate and simpler value for a given number helps to make the analysis and calculations easier while using that number. Here, Susan noted an easier value to keep a record of the distance travelled by her.

Numbers can be rounded to different digits, like, they can be rounded to the nearest ten, hundred, thousand, and so on. For example, 541 rounded to the nearest hundred is 500 because 541 is much closer to 500 than 600. While rounding a number, we need to know the answer to the question,' What are we rounding the number to?' Suppose we need to round the number 7456. When 7456 is rounded to the nearest ten, it becomes 7460, but when 7456 is rounded to the nearest thousand, then it becomes 7000. A few examples like these are given below.

Rounding Numbers to the Nearest Ten

Rounding numbers to the nearest ten means we need to check the digit to the right of the tens place, that is the ones place. For example, when we round the number 7486 to the nearest ten, it becomes 7490.

Rounding Numbers to the Nearest Hundred

Rounding numbers to the nearest hundred means we need to check the digit to the right of the hundreds place, that is, the tens place. For example, when 7456 is rounded to the nearest hundred, it becomes 7500.

Round-Up and Round-Down

While rounding is a generic term, we usually use the terms, 'round up' or 'round down' to specify if the number has increased or decreased after rounding. When the rounded number is increased, then the given number is said to be rounded up, whereas, if the rounded number is decreased, then it is said to be rounded down.

How do we decide which value is more appropriate between different approximated values of a number? Should we choose a number greater than the given number or go with the smaller one?

There are some basic rules that need to be followed for rounding numbers.

• We first need to know what our rounding digit is. This digit is the one that will ultimately be affected.
• After this, we need to check the digit to the right of this place which will decide the fate of the rounding digit.
• If the digit to the right is less than 5, we do not change the rounding digit. However, all the digits to the right of the rounding digit are changed to 0.
• If the digit to the right is 5 or more than 5, we increase the rounding digit by 1, and all the digits to the right of the rounding digit are changed to 0.

Example:

a.) If the bill at a furniture store comes to $3257, what is the rounded value of the amount to the nearest ten?

b.) If the bill comes to $3284, what would be the rounded value of this amount to the nearest ten?

Solution:

a.) $3257 needs to be rounded to the nearest ten. So, let us mark the digit in the tens place, which is 5. Now, let us check the number to the right, which is 7 in this case. Since 7 is more than 5, we will replace 5 with 6, and all the digits to the right will become 0. So, $3257 is rounded to $3260.

b.) Here, $3284 needs to be rounded to the nearest ten. So, let us mark the digit in the tens place, which is 8. Now, let us check the number to the right, which is 4 in this case. Since 4 is less than 5, 8 will remain unchanged and the remaining digits to the right will change to 0. So, $3284 is rounded to $3280.

Whole numbers are rounded off by following the same rules mentioned above. Let us apply the rules with the help of an example.

Example: Round 7234 to the nearest hundred.

• Step 1: Mark the place value up to which the number needs to be rounded. Here, 7234 needs to be rounded to the nearest hundred. So, we mark 2 which is in the hundreds place.
• Step 2: Observe and underline the digit to the right of 2, that is the tens place. Here, it is 3, so we will mark it as: 7234
• Step 3: Compare the underlined digit with 5.
• Step 4: If it is less than 5, all the digits towards its right including it will be replaced by 0 while the digit in the hundreds place (2) will remain unchanged. Therefore, 7234 will be rounded to 7200.

Note: If the number to the right of 2 was 5 or greater than 5, then all the digits to the right of 2 would become 0, and 2 would be increased by 1 changing it to 3. For example, if the given number was 7268, then it would be rounded up to 7300 (to the nearest hundred).

Fractions are numerical values that represent a part of a whole. They are written in the form of (p/q), where q is not equal to zero. A simple rule to round fractions to the nearest whole number is to compare proper fractions to 1/2. In case if it 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. Let us understand rounding off fractions to the nearest whole number using the following example.

Example: Round the given fractions to the nearest whole number:

a.) 3/4

b.) \(6 \dfrac{2}{5}\)

c.) 21/5

Solution:

a.) We can round off a proper fraction to the nearest whole number by following the simple rule of comparing it with 1/2. Since 3/4 is greater than 1/2, it will be rounded off to 1.

b.) \(6 \dfrac{2}{5}\) is a mixed fraction. Here, we will keep the whole number part aside and compare the fractional part with 1/2. So, keeping 6 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 6.

c.) 21/5 is an improper fraction, so we will convert it to a mixed fraction. This will make it \(4 \dfrac{1}{5}\). Now, we will keep the whole number part aside and compare the fractional part with 1/2. So, keeping 4 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 4.

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.

We usually round decimal numbers to the nearest tenths, hundredths, thousandths, and so on, which represent the place values after the decimal point. However, sometimes we even need to round a decimal to the nearest whole number. In this case, we check the tenths digit. If it is equal to or more than 5, then the given number is rounded up, and if the tenths digit is less than 5 then the given number is rounded down.

Example 1: Round 5.62 to the nearest whole number.

Solution: Since we need to round this decimal to the nearest whole number, we will check the tenths digit. In this case, the tenths digit is 6, which is more than 5. So, the number will be rounded to 6. In other words, 5.62 ≈ 6

In the other cases, where we need to round decimals to the nearest tenths, hundredths, or thousandths, we need to remember the simple rule of marking the number up to which we are rounding and checking the number to its right. For example, when we round decimal numbers to the nearest hundredths, we need to check the thousandths place. Similarly, if we need to round decimal numbers to the nearest tenths, we need to check the hundredths place. If the number to be checked is less than 5, then the rounding number remains unchanged, and the following digits are replaced with 0. Whereas, if the number to be checked is 5 or more than 5, then the rounding number is increased by 1 and the following digits are changed to 0. Let us understand this with an example.

Example 2: Round 0.439 to the nearest hundredths.

Solution: In this case, the digit to the right of the hundredths place, that is, the thousandths place is 9, which is more than 5. So, we will add 1 to the digit in the hundredths place, that is, 3 + 1 = 4, and write 0 in the digits to the right. So, 0.439 will be rounded to 0.44

Note: It should be noted that when we round a decimal number to the nearest hundredth, the round decimal fraction is said to be correct to two places of decimal. In other words, if we are asked to round off a number to two decimal places, it means we need to round it to the nearest hundredths. Similarly, when we are asked to round off a number to one decimal place, it means we need to round it to the nearest tenths.

Tips on Rounding Numbers:

The following tips are helpful in solving questions related to rounding numbers.

• While rounding numbers, we always need to check the digit to the right of the rounding number. If it is less than 5, the rounding number remains the same and the following digits are changed to 0. If the digit to the right is equal to or more than 5, we increase the rounding digit by 1 and the following numbers are changed to 0.
• When we round decimal numbers, we usually come across terms like round to the nearest tenths, hundredths, thousandths, and so on.
• When we are asked to round off a number to one decimal place, it means we need to round it to the nearest tenths, similarly, when we are asked to round off a number up to two decimal places, it means we need to round it to the nearest hundredths.
• When the rounded number is increased, then the given number is said to be rounded up, whereas, if the rounded number is decreased, then it is said to be rounded down.

Related Topics

Check out the following links related to rounding numbers.

• What are Numbers?
• Number Line

 

What is Rounding Numbers in Math?

Rounding a number means converting a number to a simpler value such that its value remains close to what it was. Rounding numbers makes calculation simpler and converts figures to an approximate value which is easier to remember. For example, if the population of a town is 692,769, it can be rounded to 700,000, and it would be easier to remember an approximate figure of 700,000 rather than the real figure.

What are the Rules for Rounding Off Decimal Numbers?

There are some basic rules that need to be followed for rounding decimal numbers. They are similar to rounding the other numbers, however, 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. In other words, we usually round decimal numbers to the nearest tenths, hundredths, thousandths, and so on, which represent the place values after the decimal point. Sometimes, we even round the decimal to the nearest whole number. In all these cases, we use the following rules.

• We first need to know what our rounding digit is. This digit is the one that will ultimately be affected.
• After this, we need to check the digit to the right of this place which will decide the fate of the rounding digit.
• If the digit to the right is less than 5, we do not change the rounding digit. However, all the digits to the right of the rounding digit are changed to 0.
• If the digit to the right is 5 or more than 5, we increase the rounding digit by 1, and all the digits to the right of the rounding digit are changed to 0.

For example, if we need to round 0.476 to the nearest tenths, it means we will check the digit to its right, which is the hundredths digit. In this case, it is 7 which is more than 5. Therefore, 0.476 will be rounded up to 0.5 to the nearest tenths.

What is 62 Rounded to the Nearest ten?

When 62 is rounded to the nearest 10, we need to check the digit in ones place. Here, it is 2, which is less than 5. So, 6 will remain the same, and 2 will change to 0. Therefore, 62 rounded to the nearest ten will be 60.

Where do we Use Rounding of Numbers in Real Life?

In real life, we usually round numbers whenever the exact value is not so important. For example, if we want to know the approximate amount that we spent in a grocery store, or the amount while estimating a budget, or while expressing larger figures like the population of a town. We estimate the amount to simpler numbers so that calculation becomes easier. For example, if we know that our monthly expenditure would be around $590, we can easily round the number to $600 which is a figure that is easier to remember.

How to Round Numbers to the Nearest Tenth?

If we need to round decimal numbers to the nearest tenth, we need to check the digit to the right of the digit on the tenths place, which is the hundredths place. If the number in the hundredths place is less than 5, then the rounding number remains unchanged, and the following digits are replaced with 0. Whereas, if the number to be checked is 5 or more than 5, then the rounding number is increased by 1 and the following digits are changed to 0. For example, to round 56.73 to the nearest tenth, we will check the digit in the hundredths place, which is 3 in this case. Since 3 is less than 5, 7 will remain the same and the following digits will become 0. So, 56.73 rounded to the nearest tenths will become 56.7

What is the Purpose of Rounding Numbers?

Rounding numbers means adjusting the digits of a number such that it gives an estimated result. Rounding a number gives an approximate value which is a simpler and a shorter representation of the given number. For example, if the population of a town is 498,821, it would be easier if it is expressed as 500,000. This helps in making calculations easier with a figure that is easy to remember and note. However, rounding of numbers is done in those cases where the exact value does not hold that much importance.

What is Rounding Numbers to the Nearest Ten?

When we round numbers to the nearest ten, we first mark the digit in the tens place. Then, we observe the 'ones' place, which lies to the right of the tens column. According to the rules, if the digit in the ones place is 5 or more than 5, we add 1 to the digit in the tens place, that is, we increase the tens place by 1 and write 0 in all the digits to the right. However, If the digit in the ones place is less than 5, we write 0 in the ones place and in all the places to its right, and the digit in the tens place remains the same. For example, if we need to round 389 to the nearest ten, we will check the digit in ones place. In this case, it is 9 which is more than 5. So, 8 will change to 9, and 389 will be rounded to 390.

How to Round Numbers to the Nearest 100?

In order to round numbers to the nearest hundred, we need to check the digit to its right, which is the tens place. For example, if we need to round 3270 to the nearest 100, we will check the tens place. In this case, it is 7, which means the digit in the hundreds place will be increased by 1, that is, 2 will become 3 and the remaining digits to its right will become zero. Therefore, 3270 will be rounded up to 3300.

How to Round Numbers to the Nearest Thousand?

When we round numbers to the nearest thousand, we check the digit in the hundreds place. If the digit in the hundreds place is 5 or more than 5, we increase the thousands place by 1 and write 0 in all the digits to the right. In case, if the digit in the hundreds place is less than 5, we write 0 in the hundreds place and in all the places to its right, while the digit in the thousands place remains as it is. For example, let us round 76431 to the nearest thousand. We will first check the digit in the hundreds place. In this case, it is 4, which is less than 5. So, 6 will remain as it is and all the digits to the right will become 0. Therefore, 76431 will be rounded to 76000.