**Introduction**

Numbers are very commonly used in our day to day life. In general, we need not state the exact number as an answer to the question which requires us to tell about how many. In other words, in order to ease our calculations, we often approximate the numbers to some extent. It helps us give approximate answers where exact values are not required. For instance, we may say that there are around 600 students in a school. That does not necessarily mean that there are exactly 600 students in a school. The exact number of students in the school may be somewhere around 600 which, for convenience, we have rounded off to 600. Rounding off is also termed as a shortcut method. Another example can be if you plan an event at home you can just estimate the number of guests that are supposed to attend the event. It can be a rough estimate of the number of people say 200. This does not mean that exactly 200 people will attend the event. This means we can round off numbers to the nearest place value, say 10, 100, 1000 etc.

**What are large numbers?**

Large numbers are the term that is used to refer to larger numbers that are not used in everyday life. For instance, one million, one billion etc. are all considered large numbers. Even the numbers having digits in the place value of thousands and ten thousand are considered larger numbers.

**What does rounding off mean?**

Rounding off is a type of estimation where a number is made simpler by keeping its value intact but closer to the next number. It can be done for whole numbers as well as for decimals. There are two types of rounding off –

- Rounding Up – Rounding up means the round off the given number to the next whole number.
- Rounding Down – Rounding down means the round off the given number to the previous whole number.

**Rounding large numbers to the nearest ten**

Let us now discuss rounding off large numbers to the nearest 10. To do so we shall discuss both methods – rounding up and rounding down.

**Rounding Up**

**If the number at the tens place is followed by 5, 6, 7, 8, or 9, the number is rounded up. **

**Example – We want to round off 365489 to the nearest 10.**

- Look for the digit at the ten’s place. It is 8.

- Now look for the digit to the right of the digit at the ten’s place. The number is 9

Since this number is greater than 5, we round up the number, i.e. we round it off to the nearest 10 that comes next to this number. So, 9 becomes 10 which by adding to 8 at the ten’s place, becomes 90.

Hence, the number 365489 after being rounded off to the nearest 10 is **365490**

**Note: Here we moved up the number to the nearest ten, which is why it is called rounding up.**

**Let us take another example. **

**Example – We want to round off 9427136 to the nearest 10.**

- Look for the digit at the ten’s place. It is
**3**.

- Now look for the digit to the right of the digit at the ten’s place. The number is
**6**

Since this number is greater than 5, we round up the number, i.e. we round it off to the nearest 10 that comes next to this number. So, 7 becomes 10 which by adding to 6 at the ten’s place, becomes 70.

Hence, the number 9427136 after being rounded off to the nearest 10 is **94271400**

Now that we have understood what we mean by rounding up, let us understand what is meant by rounding down.

**Rounding Down**

**If the number at the hundred’s place is followed by 0, 1, 2, 3 or 4, the number is rounded up. **

**Example – We want to round off 9532461 to the nearest 10.**

- Look for the digit at the ten’s place. It is
**6**.

- Now look for the digit to the right of the digit at the ten’s place. The number is
**1.**

Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 10 that comes before this number. So, 1 becomes 0 which by adding to 6 at the ten’s place, becomes 60.

Hence, the number 9532461 after being rounded off to the nearest 10 is **9532460****.**

**Note: Here we moved down the number to the nearest ten, which is why it is called rounding down.**

**Let us consider another example**

**Example – We want to round off 1128473 to the nearest 10.**

- Look for the digit at the ten’s place. It is 7.

- Now look for the digit to the right of the digit at the ten’s place. The number is
**3.**

Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 10 that comes before this number. So, 3 becomes 0 which by adding to 7 at the ten’s place, becomes 70.

Hence, the number 1128473 after being rounded off to the nearest 10 is **1128470****.**

**Rounding large numbers to the nearest hundred**

Let us now discuss rounding off large numbers to the nearest 100. To do so we shall discuss both methods – rounding up and rounding down.

**Rounding Up**

**If the number at the hundred’s place is followed by 5, 6, 7, 8, or 9, the number is rounded up. **

**Example – We want to round off 3954897 to the nearest 100.**

- Look for the digit at the hundred’s place. It is 8.

- Now look for the digit to the right of the digit at the hundred’s place. The number is 9

Since this number is greater than 5, we round up the number, i.e. we round it off to the nearest 100 that comes next to this number. So, 97 becomes 100 which on adding to 8 at the hundred’s places, becomes 900.

Hence, the number 3954897 after being rounded off to the nearest 100 is **3954900**

**Let us take another example. **

**Example – We want to round off 1271367 to the nearest 100.**

- Look for the digit at the hundred’s place. It is
**3**.

- Now look for the digit to the right of the digit at the hundred’s place. The number is
**6**

Since this number is greater than 5, we round up the number, i.e. we round it off to the nearest 100 that comes next to this number. So, 67 becomes 100 which by adding to 3 at the hundred’s places, becomes 400.

Hence, the number 1271367 after being rounded off to the nearest 100 is **1271400**

**Rounding Down**

**If the number at the hundred’s place is followed by 0, 1, 2, 3 or 4, the number is rounded up. **

**Example – We want to round off 6624615 to the nearest 100.**

- Look for the digit at the hundred’s place. It is
**6**.

- Now look for the digit to the right of the digit at the hundred’s place. The number is
**1.**

- Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 100 that comes next to this number. So, 15 becomes 00 which on adding to 6 at the hundred’s places, becomes 600.

Hence, the number 6624615 after being rounded off to the nearest 100 is **6624600****.**

**Let us consider another example**

**Example – We want to round off 784738 to the nearest 100.**

- Look for the digit at the hundred’s place. It is 7.

- 2. Now look for the digit to the right of the digit at the hundred’s place. The number is
**3.**

Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 100 that comes next to this number. So, 38 becomes 00 which on adding to 7 at the hundred’s places, becomes 700.

Hence, the number 784738 after being rounded off to the nearest 100 is **784700****.**

**Rounding large numbers to the nearest thousand**

Let us now discuss rounding off large numbers to the nearest 1000. To do so we shall discuss both methods – rounding up and rounding down.

**Rounding Up**

**If the number at the thousand’s place is followed by 5, 6, 7, 8, or 9, the number is rounded up. **

**Example – We want to round off 613629 to the nearest 1000.**

- Look for the digit at the thousand’s place. It is
**3**.

- Now look for the digit to the right of the digit at the thousand’s place i.e. the hundred’s place of the number. The number is
**6**

Since this number is greater than 5, we round up the number, i.e. we round it off to the nearest 1000 that comes next to this number. So, 629 becomes 1000 which on adding to 3 at the thousand’s place, becomes 4000.

Hence, the number 613629 after being rounded off to the nearest 100 is **614000**

**Let us take another example. **

**Example – We want to round off 9815810 to the nearest 1000.**

- Look for the digit at the thousand’s place. It is
**5**.

- Now look for the digit to the right of the digit at the thousand’s place. The number is
**8**

Since this number is than 5, we round up the number, i.e. we round it off to the nearest 100 that comes next to this number. So, 810 becomes 1000 which on adding to 5 at the thousand’s place, becomes 6000.

Hence, the number 985810 after being rounded off to the nearest 100 is **9816000**

**Rounding Down**

**If the number at the hundred’s place is followed by 0, 1, 2, 3 or 4, the number is rounded up. **

**Example – We want to round off 104328 to the nearest 1000.**

- Look for the digit at the thousand’s place. It is
**4**.

- Now look for the digit to the right of the digit at the thousand’s place. The number is
**3.**

Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 1000 that comes next to this number. So, 328 becomes 000 which on adding to 4 at the thousand’s place, becomes 4000.

Hence, the number 24615 after being rounded off to the nearest 100 is **104000.**

**Let us consider another example**

**Example – We want to round off 470138 to the nearest 100.**

- Look for the digit at the thousand’s place. It is
**0**.

- Now look for the digit to the right of the digit at the thousand’s place. The number is
**1.**

Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 100 that comes next to this number. So, 138 becomes 000 which on adding to 0 at the thousand’s place, becomes 0000.

Hence, the number 470138 after being rounded off to the nearest 100 is **470000****.**

**Round large numbers in decimals**

Large numbers involving decimals can be rounding up or rounded down in the same manner as we do for other decimal numbers. This means that we can round off a large number to the nearest tenth, hundredth, thousandth and so an as required. Let us discuss them one by one.

**Round Off to the Nearest Tenth**

Rounding off to the nearest tenth is also known as rounding off to one decimal place. So, how do we round off a number to the nearest tenth?

The following are the rules that must be followed for rounding off a number to the nearest tenth –

- Identify the place you want to the round to. ( In case we have the tenth place )
- Examine the digit to the right of the rounding place digit.
- If that digit is equal to 5 or greater than 5. Add 1 to the rounding place digit. If the digit is less than 5, let the rounding place digit remain as such.
- In both cases, drop all the digits to the right of the rounding place digit.

So, this means that if we want to round off the number 12365.61 to the nearest tenth, it would be 12365.60

**Round Off to the Nearest Hundredth**

Rounding off to the nearest hundredth is also known as rounding off to two decimal places. This is the most common form of rounding off that we use in solving everyday problems, especially when related to money. So, how do we round off a number to the nearest hundredth? The following are the rules that must be followed for rounding off a number to the nearest hundredth –

- Identify the place you want to the round to. ( In case we have the hundredths place )
- Examine the digit to the right of the rounding place digit.
- If that digit is equal to 5 or greater than 5. Add 1 to the rounding place digit. If the digit is less than 5, let the rounding place digit remain as such.
- In both cases, drop all the digits to the right of the rounding place digit.

So, this means that if we want to round off the number 12365.689 to the nearest tenth, it would be 12365.69

**Round Off to the Nearest Thousandth **

Rounding off to the nearest thousandth is also known as rounding off to three decimal places. So, how do we round off a number to the nearest thousandth? The following are the rules that must be followed for rounding off a number to the nearest thousandth –

- Identify the place you want to the round to. ( In case we have the thousandth place )
- Examine the digit to the right of the rounding place digit.
- If that digit is equal to 5 or greater than 5. Add 1 to the rounding place digit. If the digit is less than 5, let the rounding place digit remain as such.

So, this means that if we want to round off the number 12365.6457 to the nearest tenth, it would be 12365.646

**Some more Example on Rounding Large Numbers**

Below we have some examples demonstrating rounding off of large numbers –

**Example 1** Round off the number 6,852,718 to nearest 10, 100, 1000 and million

**Solution** 6,852,783 rounded to the nearest ten is 6,852,780

6,852,783. rounded to the nearest hundred is 6,852,800

6,852,783 rounded to the nearest thousand is 6,853,000

6,852,783 rounded to the nearest million is 7,000,000

**Example 2** Round off 121,365,587 to the nearest million

**Solution** 121,365,587 rounded off to the nearest million is 121,000,000

**Key Facts and Summary **

- Large numbers is the term that is used to refer to larger numbers that are not used in everyday life.
- Rounding off is a type of estimation where a number is made simpler by keeping its value intact but closer to the next number.
- Rounding off to the nearest tenth is also known as rounding off to one decimal place.
- Rounding off to the nearest hundredth is also known as rounding off to two decimal places.
- Rounding off to the nearest thousandth is also known as rounding off to three decimal places.

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