Chapter Notes: Rounding Off Numbers

Table of Contents
1. What is Rounding Off?
2. Place Value
3. Rules to Round Off
4. Rounding Off Whole Numbers
5. Rounding Off the Large Numbers
6. Why Do We Use Rounding?
7. Solved Examples
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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 to 40, so it rounds to 50.

Place Value

To round numbers correctly, you must know the place value of each digit. The rightmost digit is the ones place, next is tens, then hundreds, and so on.

• Ones: the digit in the rightmost place.
• Tens: the digit second from the right.
• Hundreds: the digit third 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

Follow these steps when rounding a number:

• Identify the place value you want to round to (for example, nearest ten, nearest hundred).
• Look at the digit immediately to the right of that place.

If that digit is 5 or more, round up: add 1 to the digit you are rounding and change all digits to the right to zero.
If that digit is less than 5, round down: keep the digit you are rounding the same and change all digits to the right to zero.

Examples:

• Round 86 to the nearest ten:
  The ones digit is 6. Since 6 ≥ 5, increase the tens digit by 1 and change the ones digit to 0 → 90.
• Round 73 to the nearest ten:
  The ones digit is 3. Since 3 < 5, keep the tens digit and change the ones digit to 0 → 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 estimate quickly and make numbers easier to use in daily life.

• Shopping: If a toy costs ₹198, you can round it to ₹200 to estimate the total quickly.
• Counting: If you have 342 pencils, you can say "about 300" to make it easier to talk about.
• Time: If it is 7:53, you might say it is "about 8:00" to keep things simple.

Fun Example:

You are 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:

Look at the digit in the tens place: 2.

Because 2 < 5, keep the hundreds digit the same and replace the tens and ones digits with 0.

223 rounded to the nearest hundred is 200.

Example 3: Round 12,345 to the nearest thousand.
Ans: 12,000

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.