The Concept of Operations on Multi-digit Numbers Using Rounding (Definition, Types and Examples) - BYJUS

# The Concept of Operations on Multi-digit Numbers Using Rounding

Estimation is the process of finding an approximate value of something. We can round off a number to a value near to the original value in order to make it easier to use. We can estimate the outcome of math operations like addition, subtraction, multiplication, and division by rounding off the numbers involved in the operation. ...Read MoreRead Less ## What is an estimate?

An estimate is a number that is close to the exact number.

You can estimate the sum and the differences by rounding off.

## What do you mean by rounding off a number?

Rounding means replacing a number with an approximate number that is simpler than the previous one.

To round a number to a particular place, we need to check the digit to the immediate right of that place. If the digit is 5 or greater than 5, the digit at the required place is incremented by 1. If not, the digit remains the same and all the digits to the right of that digit are replaced with zeroes.

For example:

• If 12346 is rounded to the nearest tens, the number will be 12350.
• If 12346 is rounded to the nearest hundreds, the number will be 12300.
• If 12346 is rounded to the nearest thousands, the number will be 12000.
• If 12346 is rounded to the nearest ten-thousands, the number will be 10000.

## How can we estimate sum and difference the using rounding?

The following are the steps you should follow while rounding:

• Round each number to the required place (to the nearest tens, hundreds, and so on).
• Add or subtract the rounded numbers.

For example:

Estimate 2314 + 1231. Round to the nearest tens when estimating.

Upon rounding off the numbers 2314 & 1231 to the nearest tens, we get

2314$$\rightarrow$$2310

1231$$\rightarrow$$1230 Hence, the estimated sum is 3540.

For example:

Estimate 4237 – 1532 Round to the nearest hundreds when estimating.

Upon rounding off the numbers 4237 & 1532 to the nearest hundreds, we get

4237$$\rightarrow$$4200

1532$$\rightarrow$$1500 Hence, the estimated difference is 2700.

## Solved Examples

Example 1:

Estimate 23162 – 12524. Round to nearest tens, thousands, and ten thousands to estimate in three ways.

Solution:

Upon rounding off the given numbers to nearest tens, we get

23162$$\rightarrow$$23160

12524$$\rightarrow$$12520 Similarly,

Upon rounding off the given numbers to nearest thousands, we get

23162$$\rightarrow$$23000

12524$$\rightarrow$$13000 Similarly,

Upon rounding off the given numbers to the nearest ten-thousands, we get

23162$$\rightarrow$$20000

12524$$\rightarrow$$10000 Example 2:

Estimate the sum,

17281 + 12754. Round to nearest hundreds and ten-thousands to estimate.

Solution:

Upon rounding of the given numbers according to the place values, we get

17281$$\rightarrow$$17300 (Nearest hundredths)

12754$$\rightarrow$$12800 (Nearest hundredths) Similarly,

17281$$\rightarrow$$20000

12754$$\rightarrow$$10000 Example 3:

Daisy has walked 210 yards more than Noah. If Noah has walked a total of 1520 yards, approximately how much has Daisy walked in total?

Solution:

We need to find an approximate value. Hence, we can estimate. Let us estimate to the nearest hundreds.

Noah has walked for 1520 yard

Daisy has walked for (1520 + 210) yard

Upon rounding off the distances to the nearest ten, we get

1520$$\rightarrow$$1500

210$$\rightarrow$$200

(1500 + 200) = 1700

Hence, Daisy has walked approximately 1700 yards.