Rounding off numbers are discussed here, where we need to round a number. Rounding can be done for every place value of a number.

(i) If we purchase anything and its cost is $12 and 23¢, the cost is rounded up to it’s nearest $ 12 and 23¢ is left.

(ii) If we purchase another thing and its cost is $15.78. The cost is rounded up to its nearest $16. 0.22 or 22¢ more is taken.

Similarly, any number is taken to its nearest convenient whole number. As 48 is nearer to 50 than 40, so 48 may be rounded up to 50. This is called rounding off the number. In the process of rounding of a number, it is taken to its closest whole number.

Rounding off a number makes it easier to estimate the answer in our daily life. It is also an easy way to check calculations mentally. Look at the number line below and observe how rounding of a number can be done using the number-line.

11 is closer to 10 than 20. Hence 11 is rounded down to 10. 28 is closer to 30 than 20. Hence 28 is rounded up to 30.

If the given number is between the two multiples of ten, it is rounded up to the higher multiple. So 5 is rounded up to 10.

**Note:** To round off a number to the nearest tens, we round
off it to the nearest multiple of ten.

**Consider the following examples:**

**Round off a Number to the Nearest Tens:**

**1.** Round 78 to the nearest multiple of 10.

**Solution:**

To round off a number to the nearest tens, we round off it to the nearest multiple of ten.

78 is situated between 70 and 80. The middle of 70 and 80 is 75. 78 is nearer to 80 and farther from 70.

**2.** Round 53 to its nearest multiple of 10.

**Solution:**

53 is situated between 50 and 60. The middle number between 50 and 60 is 55.

53 is before 55, so it is rounded down to 50.

(When any number is situated half way or in the middle of two convenient
whole numbers, it is rounded up to the higher whole number)

55 is rounded up to 60, 75 is rounded up to 80

54 is rounded down to 50, 74 is rounded down to 70

**3.** 37 is
rounded up to 40 because 37 is closer to 40 than 30.

**Round off a Number to the Nearest Hundreds:**

To round off a number to the nearest hundreds, we round off it to the nearest multiple of hundred.

**For Example:**

225 is nearer to 200 than 300. So, 225 is rounded down to 200.

**Round off Number to the Nearest Thousands**

To round off number to the nearest thousands, we round off it to the nearest multiple of thousand.

**For example:**

5431 is nearer to 5000 than 6000. So, 5431 is rounded down to 5000.

Questions and Answers on Rounding off Numbers:

**I. Round
off the following numbers to nearest tens:**

(i) 39

(ii) 183

(iii) 102

(iv) 209

(v) 1268

(vi) 5186

(vii) 9549

(viii) 8911

**Answers:**

(i) 40

(ii) 180

(iii) 100

(iv) 210

(v) 127068

(vi) 5190

(vii) 9550

(viii) 8910

**II. Round
off the following numbers to nearest hundreds:**

(i) 3081

(ii) 5232

(iii) 4884

(iv) 6012

**Answers:**

(i) 3100

(ii) 5200

(iii) 4900

(iv) 6000

**III. Round
off the following numbers to nearest thousands:**

(i) 4128

(ii) 2854

(iii) 14585

(iv) 27102

**Answers:**

(i) 4000

(ii) 3000

(iii) 15000

(iv) 27000

**IV. Using number line, round off following numbers to the
nearest tens:**

(i) Round 72 to the nearest tens.

72 is closer to _______. Hence it is rounded down to _______.

(ii) Round 39 to the nearest tens.

39 is closer to _______. Hence it is rounded down to _______.

**Answer:**

**IV. **(i) 72 is closer to 70. Hence it is rounded down to 70.

(ii) 39 is closer to 40. Hence it is rounded up to 40.

**V. Round the given numbers to the nearest tens:**

(i) 42

(ii) 67

(iii) 89

(iv) 47

(v) 56

(vi) 78

**Answer:**

**V. **(i) 40

(ii) 70

(iii) 90

(iv) 50

(v) 60

(vi) 80

**Related Concept **

**● **** Numbers Showing on Spike Abacus.**

**● **** 1 Digit Number on Spike Abacus.**

**● **** 2 Digits Number on Spike Abacus.**

**● ****3 Digits Number on Spike Abacus.**

**● ****4 Digits Number on Spike Abacus.**

**● **** 5 Digits Number on Spike Abacus.**

**● **** Problems Related to Place Value.**

**● ****Example on Comparison of Numbers.**

**● **** Successor and Predecessor of a Whole Number.**

**● **** Formation of Numbers with the Given Digits.**

**● **** Formation of Greatest and Smallest Numbers.**

**● ****Examples on the Formation of Greatest ****and the Smallest Number.**

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