**Estimation and Rounding Off**

**Rounding Off**

Rounding off a number refers to the process of making a number simpler such that itsâ€™ value remains close to or the same as the nearest ten or nearest hundred.

The result obtained after rounding off a number is less accurate. but it is easier to use.

Here we will learn about

- Rules of rounding off numbers
- Rounding off numbers to the nearest ten
- Rounding off numbers to the nearest hundred
- Rounding off Sum and Difference
- Rounding off product

Rules for Rounding Off Numbers

The rules for rounding off numbers are as follows.

- First, we need to know what our rounding digit is.
- After that, check the digit right to this place. The digit plays a very important role in rounding off a number.
- If this digit is less than 5, then we do not change the rounding digit. But all the digits right to the rounding digit are changed to 0.
- If this digit is equal to or more than 5, then we increase the rounding digit by 1, and all the digits to the right of the rounding digit are changed to 0.

Examples:

- Round of the number 86 to the nearest ten.
- Round of the number 62 to the nearest ten.
- Round of the number 45 to the nearest ten.

**Answer:**

- The number right to the tenâ€™s place of the number 86 is 6,
6 > 5
So, after rounding the number to the nearest ten it will be 90.

- The number right to the tenâ€™s place of the number 62 is 2,
2 < 5
So, after rounding the number to the nearest ten it will be 60.

- The number right to the tenâ€™s place of the number 45 is 5,
So, after rounding the number to the nearest ten it will be 50.

Rounding Off Numbers to the Nearest Ten

- To round off numbers to the nearest ten, check the number right to the tenâ€™s place.
- Then follow the rules of rounding off as described above.

Let us discuss with an example.

Examples:

- Round of the number 986 to the nearest ten.
- Round of the number 762 to the nearest ten.
- Round of the number 145 to the nearest ten.

**Answer:**

- The number right to the tenâ€™s place of the number 986 is 6, 6 > 5
So, after rounding the number to the nearest ten it will be 990.

- The number right to the tenâ€™s place of the number 762 is 2,2 < 5
So, after rounding the number to the nearest ten it will be 760.

- The number right to the tenâ€™s place of the number 145 is 5,
So, after rounding the number to the nearest ten it will be 150.

Rounding Off Numbers to the Nearest Hundred

- To round off numbers to the nearest hundred, check the number right to the hundredâ€™s place.
- Then follow the rules of rounding off as described above. Let us discuss with an example.

Examples:

- Round off the number 546 to the nearest hundred.
- Round off the number to 343 the nearest hundred.
- Round off the number 255 to the nearest hundred.

**Answer:**

- The number right to the hundredâ€™s place of the number 546 is 4,

4 < 5So, after rounding the number to the nearest hundred it will be 500.

- The number right to the hundredâ€™s place of the number 343 is 4,

4 < 5So, after rounding the number to the nearest hundred it will be 300.

- The number right to the hundredâ€™s place of the number 255 is 5,

5 = 5So, after rounding the number to the nearest hundred it will be 300.

Rounding Off Sum and difference

- In the case of two-digit numbers,
- Round of both the addends to their nearest ten and then add the numbers you get after round off.
- Round of the minuend and subtrahend to their nearest ten and then subtract the numbers you get after round off.

Examples:

a) 86 + 42 b) 94 â€“ 33

**Answer:**- Rounding off 86 to the nearest ten, we get 90

Rounding off 42 to the nearest ten, we get 40

90 + 40 = 130

**Check:**86 + 42 = 128

If 128 is rounded off to its nearest ten, we get 130. - Rounding off 94 to the nearest ten, we get 90

Rounding off 33 to the nearest ten, we get 30

90 - 30 = 60

**Check:**94 - 33 = 61

If 61 is rounded off to its nearest ten, we get 60.

- In the case of three-digit numbers,
- i) Round of both the addends to their nearest ten and then add the numbers you get after round off.

ii) Round of the minuend and subtrahend to their nearest ten and then subtract the numbers you get after round off.Examples:

a)762 + 849 b) 768 â€“ 641

**Answer:**- Rounding off 762 to the nearest ten, we get 760

Rounding off 849 to the nearest ten, we get 850

760 + 850 = 1610

**Check:**762 + 849 = 1611

If 1611 is rounded off to its nearest ten, we get 1610. - Rounding off 768 to the nearest ten, we get 770

Rounding off 641 to the nearest ten, we get 640

770 - 640 = 130

**Check:**768 â€“ 641= 127

If 127 is rounded off to its nearest ten, we get 130.

- Rounding off 762 to the nearest ten, we get 760
- i) Round of both the addends to their nearest hundred and then add the numbers you get after round off.

ii) Round of the minuend and subtrahend to their nearest hundred and then subtract the numbers you get after round off.Examples:

a)762 + 859 b) 768 â€“ 641

**Answer:**- Rounding off 762 to the nearest hundred, we get 800

Rounding off 859 to the nearest hundred, we get 900

800 + 900 = 1700

**Check:**762 + 859 = 1621

If 1621 is rounded off to its nearest hundred, we get 1600.

Clearly, the answer is not accurate enough. - Rounding off 768 to the nearest hundred, we get 800

Rounding off 641 to the nearest hundred, we get 600

800 - 600 = 200

**Check:**768 â€“ 641= 127

If 127 is rounded off to its nearest hundred, we get 100.

Clearly, the answer is not accurate enough.

- Rounding off 762 to the nearest hundred, we get 800

- i) Round of both the addends to their nearest ten and then add the numbers you get after round off.

Rounding Off Product

In the case of two-digit numbers,

Round of the multiplicand and multiplier to their nearest ten and then multiply the numbers you get after round off.

Examples: 48 Ă— 33

**Answer:**

- Rounding off 48 to the nearest ten, we get 50

Rounding off 33 to the nearest ten, we get 30

50 Ă— 30 = 1500

**Check:** 48 Ă— 33 = 1584

If 1584 is rounded off to its nearest ten, we get 1580.

If 1584 is rounded off to its nearest hundred, we get 1600.

Clearly, the answer is not accurate enough.

Round-Up and Round-Down

While rounding off a number, we usually use the term round up or round down.

- When the number is increased after rounding off, we call it round-up.
- When the number is decreased after rounding off, we call it round-down.

Examples: Round off the numbers 76 and 93.

**Answer:**

Rounding off 76 to the nearest ten we get 80. So, 76 is round-up to 80 as the number is increased.

Rounding off 93 to the nearest ten we get 90. So, 93 is round-down to 90 as the number is decreased.