Estimation and Rounding Off

This chapter will introduce the concept of rounding off the number to the nearest hundred or rounding off to the nearest 10 to students. Also, they will learn about the rules of rounding off numbers and what is called round up and round down. Digits in a number and their place value play an essential role in this chapter.

The learning concept will all about

• Applying the rules of rounding off numbers
• To use the concept of rounding off daily to make calculations easier.

The concept is explained to class 3 students using examples, illustrations and concept maps. At the end of the page, two printable worksheets with solutions are attached for the students.

Download the worksheets and the printable solutions and assess your knowledge.

What Is Rounding Off?

Rounding off a number refers to the process of making a number simpler such that its’ 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.

Example:

1. Round of the number 86 to the nearest ten.
2. Round of the number 62 to the nearest ten.
3. Round of the number 45 to the nearest ten.

Answer:

1. The number right to the ten’s place of the number 86 is 6, 6 > 5

   So, after rounding the number to the nearest ten it will be 90.

2. The number right to the ten’s place of the number 62 is 2, 2 < 5

   So, after rounding the number to the nearest ten it will be 60.

3. The number right to the ten’s place of the number 45 is 5,

   So, after rounding the number to the nearest ten it will be 50.

Round Off to the Nearest 10

• To round off numbers to the nearest ten, check the number right to the ten’s place.
• Then follow the rules of rounding off as described above.

Let us discuss with an example.

Example:

1. Round of the number 986 to the nearest ten.
2. Round of the number 762 to the nearest ten.
3. Round of the number 145 to the nearest ten.

Answer:

1. The number right to the ten’s place of the number 986 is 6, 6 > 5

   So, after rounding the number to the nearest ten it will be 990.

2. The number right to the ten’s place of the number 762 is 2,2 < 5

   So, after rounding the number to the nearest ten it will be 760.

3. The number right to the ten’s place of the number 145 is 5,

   So, after rounding the number to the nearest ten it will be 150.

Round Off the Number to the Nearest 100

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

Example:

1. Round off the number 546 to the nearest hundred.
2. Round off the number to 343 the nearest hundred.
3. Round off the number 255 to the nearest hundred.

Answer:

1. The number right to the hundred’s place of the number 546 is 4,
   4 < 5

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

2. The number right to the hundred’s place of the number 343 is 4,
   4 < 5

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

3. The number right to the hundred’s place of the number 255 is 5,
   5 = 5

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

Rounding Off Sum and difference

• In the case of two-digit numbers,
  1. Round of both the addends to their nearest ten and then add the numbers you get after round off.
  2. 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 – 33

  Answer:

  1. 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.
  2. 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,
  1. 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 – 641

     Answer:

     1. 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.
     2. 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 – 641= 127
        If 127 is rounded off to its nearest ten, we get 130.
  2. 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 – 641

     Answer:

     1. 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.
     2. 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 – 641= 127
        If 127 is rounded off to its nearest hundred, we get 100.
        Clearly, the answer is not accurate enough.

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 × 33

Answer:

1. Rounding off 48 to the nearest ten, we get 50

Rounding off 33 to the nearest ten, we get 30

50 × 30 = 1500

Check: 48 × 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.