Rounding Off Numbers Chapter Notes | Mathematics for Class 5 PDF Download

What is Rounding Off?

• Rounding off means changing a number to a simpler number that is close to the original value. 
• Example:
  Number: 47
  Rounding to the nearest ten: 47 is closer to 50 than 40, 
  So it rounds to 50.

Place Value

To round off numbers, you need to understand place values. Each digit in a number has a place value, such as ones, tens, hundreds, etc.

• Ones: The digit in the rightmost place.

• Tens: The digit in the second place from the right.

• Hundreds: The digit in the third place from the right.

• For Example, In the number 536:
  6 is in the ones place.
  3 is in the tens place.
  5 is in the hundreds place.

Rules to Round Off

Step 1:  Identify the Place Value

Decide which place value you want to round to (e.g., nearest whole number, nearest ten, nearest hundred).

Step 2: Look at the digit to the right of that place:

1. If it’s 5 or more, round up (add 1 to the digit you’re rounding).
Round Up: Increase the rounding digit by 1 and change all digits to the right to zero.
Examples:
Round 86 to the nearest ten:

• The tens digit is 8.

• The ones digit is 6.

• Since 6 is greater than 5, increase the tens digit by 1 (8 becomes 9).

• Result: 90.

2. If it’s less than 5, round down (keep the digit the same).
Round Down: Keep the rounding digit the same and change all digits to the right to zero.
Example:
Round 73 to the nearest ten:

• The tens digit is 7.

• The ones digit (to the right) is 3.

• Since 3 is less than 5, keep the tens digit as 7 and replace the ones digit with 0.

• Result: 70

Rounding Off Whole Numbers

(i) Rounding off to the nearest 10

• If the digit in the ones place is 0, 1, 2, 3, or 4 (i.e. < 5) then replace ones place by ‘0
• 
•  If the digit in the ones place is 5, 6, 7, 8 or 9 (i.e. > 5 or = 5, but < 10), then replace ones digit by ‘0’ and add 1 to the tens place
• 

(ii) Rounding off to the nearest 100

• If the digit in the tens place is 0, 1, 2, 3, or 4 (i.e. < 5) then replace ones and tens places by ‘0’
• 
•  If the digit in the tens place is 5, 6, 7, 8 or 9 (i.e. > 5 or = 5, but < 10), then replace ones and tens places by ‘0’ and add 1 to the hundreds place.
• 

(iii) Rounding off to the nearest 1000

• If the digit in the hundred place is 0, 1, 2, 3, or 4 (i.e. < 5) then replace ones, tens and hundred places by ‘0’.
  
•  If the digit in the hundreds place is 5, 6, 7, 8 or 9 (i.e. > 5 or = 5, but < 10), then replace ones, tens and hundred places by ‘0’ and add 1 to the thousands place.
• 

Rounding Off the Large Numbers

(i)  Rounding off to the nearest 10,000

• If the digit in the thousands place is 0, 1, 2, 3, or 4 (i.e. < 5) then replace ones, tens, hundred and thousand places by ‘0’.
• 
•  If the digit in the thousands place is 5, 6, 7, 8 or 9 (i.e. > 5 or = 5, but < 10), then replace ones, tens, hundred and thousands places by ‘0’ and add 1 to the ten thousands place.
• 

(ii) Rounding off to the nearest 1,00,000

• If the digit in the ten thousands place is 0, 1, 2, 3, or 4 (i.e. < 5) then replace ones, tens, hundred, thousand and ten thousand places by ‘0’.
• 
• If the digit in the ten thousands place is 5, 6, 7, 8 or 9 (i.e. > 5 or = 5, but < 10), then replace ones, tens, hundreds, thousands and ten thousands places by ‘0’ and add 1 to the lakh place.
  
• 

Why Do We Use Rounding?

Rounding helps us in real life! Here are some examples:

• Shopping: If a toy costs ₹198, you can round it to ₹200 to estimate quickly.

• Counting: If you have 342 pencils, you can say “about 300” to make it easier.

• Time: If it’s 7:53, you might say it’s “about 8:00” to keep things simple.

Fun Example:
You’re buying 47 apples. 
To estimate the cost, round 47 to 50. 
If each apple costs ₹10, you can quickly guess the total as 50 × ₹10 = ₹500.

Solved Examples

Example 1: Round 347 to the nearest ten.
Ans: 350

Sol:
Step 1: Look at the digit in the ones place (7).

Step 2: Since 7 is more than 5, we round up.

Therefore the answer rounds up to 350

Example 2: Round 223 to the nearest hundred.
Ans: 200

Sol:
Step 1: Look at the digit in the tens place (3).
Step 2: Since 2 is less than 5, we round down.
Therefore the answer rounds down to 200.

Example 3: Round 12,345 to the nearest thousand.
Ans: 12000

Sol:
Step 1: Look at the digit in the hundreds place (3).
Step 2: Since 3 is less than 5, we round down.
Therefore 12,345 rounds down to 12,000.

Example 4: Round 876,543 to the nearest hundred thousand.
Ans: 900,000

Sol:
Step 1: Look at the digit in the ten thousand place (7).
Step 2: Since 7 is 5 or more, we round up.
Therefore , 876,543 rounds up to 900,000.