Rounding the numbers helps us to get the required information while we approximate a number. Whereas for quick calculation use estimation. To estimate Sum, Difference, or Product we first need to round off the given number the nearest tens, hundreds, thousand, million, or any other ten multiple numbers, after doing so we need to apply the required mathematical operations.

Do Check:

### Estimating the Sum of Two Numbers

Whenever we are estimating the sum, we should have an idea of the place to which the rounding is needed.

Let’s go through few examples for better understanding.

**Example 1:**

Estimate 1398 + 526?

**Solution:**

We should first round off these numbers to the nearest ten multiple.

1398 can be rounded off to 1400

526 can be rounded off to 500

Estimated Sum:

1400 + 400 = 1900

**Example 2:**

Estimate 47 + 74?

**Solution:**

We should first round off these numbers to the nearest ten multiple.

47 can be rounded off to 50

74 can be rounded off to 70

Estimated sum:

50 + 70 = 120

**Example 3:**

Estimate 12346 + 14672?

**Solution:**

We should first round off these numbers to the nearest ten multiple.

12346 can be rounded off to 12350

14672 can be rounded off to 14670

Estimated sum:

12350 + 14670 = 27020

**Example 4:**

Minnie spent 4876/- on groceries and 6782/- on shopping. While discussing the expenditure she says that she approximately spent 4880/- on groceries. and 6790 on shopping. What is the estimated sum of her expenditure?

**Solution:**

Actual expenditure on groceries = 4876

4876 can be rounded off to 4880 as Minnie mentioned

Actual expenditure on shopping = 6782

6782 can be rounded off to 6790 as Minnie mentioned

So now estimated sum = 4880 + 6790

= 11,670.

### Estimating the Difference of Two Numbers

Whenever we are estimating the difference, we should have an idea of the place to which the rounding is needed.

Let’s go through few examples for better understanding.

**Example 1:**

Estimate 67 – 32

**Solution:**

67 can be rounded off to 70

32 can be rounded off to 30

Estimated difference: 70 – 30

= 40

**Example 2:**

Estimate 892- 576

**Solution:**

567 can be rounded off to 570

892 can be rounded off to 890

Estimated difference: 890 – 570

=320.

**Example 3:**

Estimate 6789 – 1234

**Solution:**

6789 can be rounded off to 6790

1234 can be rounded off to 1230

Estimated difference: 6790 – 1230

= 5560

**Example 4: **

In Delhi, 25856 people travel by bus in the morning and 32147 in the evening. What is the estimated difference between the people that travel by bus every day?

**Solution:**

The actual number of people traveling in the morning by bus = 25856

25856 can be rounded off to 25860.

The actual number of people traveling in the evening by bus= 32147

32147 can be rounded off to 32150

So now estimated difference = 32150 + 25860

= 6,290.

### Estimating the Product of Two Numbers

Whenever we are estimating the product, we should round off each factor to its greatest place, after doing so we have to multiply the rounded factors.

Let’s go through few examples for better understanding.

**Example 1:**

Estimate 62 * 12

**Solution:**

62 can be rounded off to 60

12 can be rounded off to 10

Estimated product: 60 * 10

= 600

**Example 2:**

736 * 31

**Solution:**

736 can be rounded off to 740.

31 can be rounded off to 30

Estimated product: 740 * 30

= 22200.

**Example 3:**

4567 * 891

**Solution:**

4567 can be rounded off to 4570.

891 can be rounded off to 890.

Estimated product: 4570 * 890.

= 4,067,300.

**Example 4:**

In a city library, there are 9954 science books on each floor. That particular library is a 6 stored building. Calculate and find the estimated numbers of science books in that library.

**Solution:**

The actual number of books = 9954

9954 can be rounded off to 9950

Number of floors in library = 6

6 can be rounded to 10

Estimated product = 9950 * 10

= 99500.

#### Choose the Correct Answer by Estimating

1. A library has 987689 books. Choose what is the estimated number of books in the library?

(a) 987690

(b) 987680

**Solution:**

987689 should be rounded off to the nearest ten multiple.

So 987689 can be rounded off to 987690.

(a) 987690

2. Tom has 568 milk packs and Jerry has 644 milk packs. Calculate total estimated milk packets.

(a) 1212

(b) 1210

**Solution:**

568 can be rounded off to 570

644 can be rounded off to 640

Total number of milk packs = 570 + 640

= 1210.

(b) 1210

3. Each pack of crayons contain 12 different colors, there is 367 crayon packet. What is the count of the total estimated crayons?

(a) 3700

(b) 4,404

**Solution:**

Number of crayons in one pack = 12

12 can be rounded off to 10

Total number of crayon packs = 367

367 can be rounded off to 370

Total estimated number of crayons = 370 * 10

=3700

(a) 3700