Session 3: Estimation of Numbers (Rounding Off Method) – Rules, Steps and Examples

What is Estimation?

There are situations in our daily lives when it is inconvenient, difficult, or even impossible to report the exact number of items in a group or set. When we cannot report an exact number, we can use an estimate. An estimate can be a rounded number that tells how much or how many. Sometimes we put forth an estimated value to make calculations easier and more realistic.

Here are some examples of estimation:

• There are over 34,000 recognized fish species worldwide, and they inhabit a wide range of watery habitats.
• While there were 100,000 wild tigers a hundred years ago, by 2020, their numbers had gone down to 3,900.
• The age of the oldest elephant on record, Dakshayani, was 90 years. It died in 2019.

One very simple form of estimation is rounding. Rounding is often the key process we use to estimate a number quickly. With this process, we make a large number simpler by expressing in terms of the nearest unit, ten, hundred or thousand places.

Rounding Off a Number to the Nearest 10

To find out the multiple of 10 nearest the given number is called rounding off the given number to the nearest 10. 

Consider the numbers 62 and 186.

If we plot these numbers on a number line, we find that the closest ten less than 62 is 60, and the closest ten greater than 62 is 70.

Since 62 is closer to 60 than 70, round 62 to 60, correct to the nearest tens.

If we consider 186, we find that the closest ten less than 186 is 180, and the closest ten greater than 186 is 190.

Since 186 is closer to 190 than 180, round 186 to 190, correct to the nearest tens.
It is impractical to first represent the number on a number line and then round off, so we follow a more general procedure.

Steps to Round Off a Number to the Nearest 10

To round off a number to the nearest 10, we follow the following steps:

Step 1: Underline the digit in the tens place.

Step 2: Circle the next digit on its right, i.e. ones digit. If the digit is 4 or less, do not change the underlined digit. If the digit is 5 or greater, add 1 to the digit in the tens place.

Step 3: Put a zero in the ones place as a placeholder.

1) Round off each of the following numbers to the nearest tens.

i. 237

ii. 51

i. The given number is 237.

Its ones digit is 7, which is greater than 5. So, add 1 to the digit in the tens place.

  ∴ Rounded number = 240

ii. The given number is 51.

Its ones digit is 1, which is less than 5. So, replace the ones digit by 0 and keep the other digits as they are.

  ∴ Rounded number = 50

Rounding Off a Number to the Nearest 100

To find out the multiple of 100 nearest to the given number is called rounding off the given number to the nearest 100.

Consider the numbers 467 and 1,123.

If we plot 467 on a number line, the closest hundred less than 467 is 400, and the closest hundred greater than 467 is 500.

Since 467 is closer to 500 than 400, round 467 to 500, correct to the nearest hundreds.

If we plot 1,123 numbers on a number line, the closest hundred less than 1,123 is 1,100, and the closest hundred greater than 1,123 is 1,200.

Since 1,123 is closer to the 1,100 than to 1,200, round 1,123 to 1,100, correct to the nearest hundreds.

Steps to Round Off a Number to the Nearest 100

To round off a number to the nearest 100, we follow the following steps:

Step 1: Underline the digit in the hundreds place.

Step 2: Circle the next digit on its right, i.e. tens digit. If the digit is 4 or less, do not change the underlined digit. If the digit is 5 or greater, add 1 to the digit in the hundreds place.

Step 3: Put a zero in the tens and ones place as a place holder.

2) Round off each of the following numbers to the nearest hundreds.

i. 186

ii. 5,728

i. The given number is 186.

Its tens digit is 8, which is greater than 5. So, add 1 to the digit in the hundreds place and replace the tens and ones digit by 0. Keep the other digits as they are.

∴ Rounded number = 200

ii. The given number is 5,728.

Its tens digit is 2, which is less than 5. So, replace the tens and ones digit by 0 and keep the other digits as they are.

∴ Rounded number = 5,700

Round Off a Number to the Nearest 1000

To find out the multiple of 1000 nearest to the given number is called rounding off the given number to the nearest 1000.

Consider the numbers 23,692 and 7,419.

If we plot these numbers on a number line, we find that the closest thousand less than 23,692 is 23,000 and the closes thousand greater than 23,692 is 24,000

Since 23,692 is closer to 24,000 than to 23,000, round 23,692 to 24,000, correct to the nearest thousands.

If we consider 7,419, we find that the closest thousand less than 7,419 is 7,000 and the closest thousand greater than 7,419 is 8,000.

Since 7,419 is closer to 7,000 than 8,000, round 7,419 to 7,000, correct to the nearest thousands.

Steps to Round Off a Number to the Nearest 100

To round off a number to the nearest 1000, we follow the following steps:

Step 1: Underline the digit in the thousands place.

Step 2: Circle the next digit on its right, i.e. hundreds digit. If the digit is 4 or less, do not change the underlined digit. If the digit is 5 or greater, add 1 to the digit in the thousands place.

Step 3: Put a zero in the hundreds, tens and ones places as a placeholder.

3) Round off each of the following numbers to the nearest thousands.

i. 99,365

ii. 2,20,831

i. The given number is 99,365

The hundreds digit is 3, which is less than 5. So, replace the hundreds, tens and ones digit by 0 and keep the other digits as they are.

∴ Rounded number = 99,000

ii. The given number is 2,20,831

The hundreds digit is 8, which is greater than 5. So, add 1 to the digit in the thousand places and replace the hundreds, tens and ones digit by 0. Keep the other digits as they are.

∴ Rounded number = 2,21,000

Estimating Sum, Difference, Product and Quotient

When measuring something, it is an excellent habit to estimate the measurement to check your answer.

Similarly, estimating the answer is also an excellent habit when we have to do calculations. It saves time, and we can better picture things in a simpler way.

Thus, there are many situations where we use estimation to get a quick and rough answer. This estimated value is obtained by rounding off the numbers involved in the arithmetic problem and getting an approximate but satisfactory answer through mental calculation.

You can estimate sums (the answers to addition problems), differences (the answers to subtraction problems), products (the answers to multiplication problems), quotients (the answer to division problems) of numbers. The first step in estimating a sum, a difference, a product or a quotient is to round the numbers to the nearest tens, hundreds, thousands, etc.

When rounding, follow these rounding rules:

• If the number being rounded is less than 5, round down.
• If the number being rounded is 5 or greater, round up.

To see how rounding can help with estimating, consider the following examples:

Estimating Sum

4) Give an estimate for the sum 5,632 + 4,043 rounded to the nearest thousands.

Note: The symbol ≈ means is approximately equal to.

Estimating Difference

5) Give an estimate for the difference of 9,975 – 7,544 rounded to the nearest hundreds.

Estimate Product

6) Estimate the product of 321 × 286 by rounding to the nearest hundreds.

Note: If both multipliers end in 50 or halfway numbers, round one number up and one number down to better estimate the product.

7) Estimate the product of 45 × 25 by rounding to the nearest tens.

Rounding one number up and one down, we have

We can also round the first number down and the second number up and get this.

In either case, the estimated product is closer than if we round both numbers up, which is the standard rule.

Estimate Quotient

8) Estimate the quotient of 1,582 ÷ 431 by rounding to the nearest hundred.

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Estimation of Numbers (Rounding Off Method) – Examples

Example 1

Round off each of the following numbers to the nearest tens.

i. 98

ii. 543

i. The given number is 98.

  Its ones digit is 8, which is greater than 5. So, add 1 to the digit in the tens place.

  ∴ Rounded number = 100

ii. The given number is 543.

  Its ones digit is 3, which is less than 5. So, replace the ones digit by 0 and keep the other digits as they are.

  ∴ Rounded number = 540

Example 2

Round off each of the following numbers to the nearest hundreds.

i. 7,076

ii. 62,935

i. The given number is 7076.

Its tens digit is 7, which is greater than 5. So, add 1 to the digit in the hundreds place and replace the tens and ones digit by 0. Keep the other digits as they are.

∴ Rounded number = 7,100

ii. The given number is 62935.

Its tens digit is 3, which is less than 5. So, replace the tens and ones digit by 0 and keep the other digits as they are.

∴ Rounded number = 62,900

Example 3

Round off each of the following numbers to the nearest thousands.

i. 34,476

ii. 1,19,925

i. The given number is 34,476

The hundreds digit is 4, which is less than 5. So, replace the hundreds, tens and ones digit by 0 and keep the other digits as they are.

∴ Rounded number = 34,000

ii. The given number is 1,19,925

The hundreds digit is 9, which is greater than 5. So, add 1 to the digit in the thousand places and replace the hundreds, tens and ones digit by 0. Keep the other digits as they are.

∴ Rounded number = 1,20,000

Example 4

Tina evaluates 863 × 112 using a calculator and says the answer is 9,665. Without using the actual calculation, use estimation to determine whether Tina’s answer is reasonable.

Tina needs to estimate the product of 863 and 112.

First, round 863 to the nearest hundred. Since the number in the tens place is greater than 5, round up. 863 rounds to 900.

Next, round 112 to the nearest hundred. Since the number in the tens place is less than 5, round down. 112 rounds to 100.

Finally, multiply the rounded values:

900×100=90000
⇒863×112≈90000

∴ Tina’s answer is wrong.