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Last modified on August 3rd, 2023

The standard way we approximate a number when given a collection of any object, by mentally considering the collection as in groups of tens, hundreds, or thousands, is rounding numbers. Rounding whole numbers is a way by which we make numbers look good. It is a handy way to estimate the numbers in the rounded form instead of expressing them in the exact form.

Numbers that look nice in our minds end with a zero, such as 10, 30, or 200.

Thus, rounding numbers usually means we will try to put zero(s) at the end.

We can round any number to its nearest ten, hundred, thousand, or ten-thousand.

Rounded numbers are the approximate values; they will never give exact answers.

**Round 62 to the nearest ten**

- 62
- 6 is the digit in 10th place, 2 is the unit digit
- 2 < 5, so add nothing to 6.
- Replace 2 with 0
- The rounded off result of 62 to the nearest ten is 60

**Round 67 to the nearest ten**

- 67
- 6 is the digit in 10th place, 7 is the unit digit
- 7 > 5, so add 1 to 6.
- Replace 7 with 0
- The rounded off result of 67 to the nearest ten is 70

Steps to round whole numbers:

- Locate the position (10, 100, or 1000) of the digit to be rounded off.
- Locate the digit to the exact right of the digit we will round off.
- Rounding Down: If the digit is less than 5, replace it and all the digits to its right with zeros. Leave the round-off digit as it is.
- Rounding Up: If digit is 5 or larger, replace it with zeros and all the digits to its right. Increase the round-off digit by 1.

Let us see how to round the numbers to the nearest tens, hundreds, and thousands.

When rounding a whole number to its nearest ten, we need to locate the last digit at the unit place.

**Case 1** – The last digit is 1, 2, 3, or 4, then replace it with 0 (zero), and keep the digit in the 10th place unchanged.

**Case 2** – The last digit is 5 or larger, then replace it with 0 (zero), and add 1 to the digit in the 10th place.

Rounding 241 – Here the digit in the 10th place is 4, the digit in the unit place is 1 which is <5.

So we change 1 to 0 and keep 4 unchanged. Thus, the rounded-off result is 240.

Now, Rounding 346 – Here the digit in the 10th place is 4, the digit in the unit place is 6 which is >5.

So we change 6 to 0 and add 1 to 4. Thus, the rounded-off result is 350.

When rounding a whole number to its nearest hundred, we need to locate the last 2 digits.

**Case 1** – The last 2 digits is 49 or less, then replace the last 2 digits with 0s (zeroes), and keep the digit in the 100th place unchanged.

**Case 2** – The last 2 digits are 50 or larger, then replace the last 2 digits with 0s (zeroes), and add 1 to the digit in the 100th place.

Rounding 817 – Here the 2 digits after 8 is 17 which is <50.

So we replace 17 with 00 and keep 8 unchanged. Thus, the rounded-off result is 800.

Rounding 689 – Here the 2 digits after 6 is 89 which is >50.

So we replace 89 with 00 and add 1 to 6. Thus, the rounded-off result is 700.

When rounding a whole number to its nearest thousand, we need to locate the last 3 digits.

**Case 1** – The last 3 digits is 499 or less, then replace the last 3 digits with 0s (zeroes), and keep the digit in the 1000th place unchanged.

**Case 2** – The last 3 digits are 500 or larger, then replace the last 3 digits with 0s (zeroes), and add 1 to the digit in the 1000th place.

Rounding 39,450 – Here the 3 digits after 9 is 450 which is <500.

So we replace 450 with 000 and keep 9 unchanged. Thus, the rounded-off result is 39,000.

Rounding 61,728 – Here the 3 digits after 1 is 728 which is >500.

So we replace 728 with 000 and add 1 to 1. Thus, the rounded-off result is 62,000.

**Round 564 to the nearest ten.**

Solution:

As we know,

4<5

So, the rounded off result of 564 = 560

**Round 929 to the nearest ten.**

Solution:

As we know,

9>5

So, the rounded off result of 929 = 930

**Round 2,901 to the nearest hundred.**

Solution:

As we know,

01<50

So, the rounded off result of 2,901 = 2,900

**Round 9,456 to the nearest hundred.**

Solution:

As we know,

56>50

So, the rounded off result of 9,456 = 9,500

**Round 49,287 to the nearest thousand.**

Solution:

As we know,

287<500

So, the rounded off result of 49,287 = 49,000

**Round 84,788 to the nearest thousand.**

Solution:

As we know,

788>500 So, the rounded off result of 84,788 = 85,000

Last modified on August 3rd, 2023

Very wonderful teaching