They are only the approximate or closer values to the actual ones. This is the reason, why we generally use words like “about”, “nearly” and “approximately”. These numbers are only the estimation of the actual value. The word ‘about’ denotes the number not exactly, but a little more or less. This value is called the estimated value.

**Estimation
of numbers**

● Nearly 60,000 people watched the Republic day
parade at Rajpath, New Delhi.

● About 2,80,000 people of various countries died
due to earthquake and Tsunami on 26th December 2004 in the Indian ocean.

● The India-Pakistan cricket match was viewed by
about 30 million cricket fans in the Television all over the world.

We often come across statements like these in TV
channels and dailies. Do these news items, give the exact numbers? No. The numbers
mentioned are not accurate. They are only the approximate or closer values to the
actual ones. This is the reason, why we generally use words like “about”, “nearly”
and “approximately”. These numbers are only the estimation of the actual value.
The word ‘about’ denotes the number not exactly, but a little more or less. This
value is called the estimated value.

The actual figure, though not exactly possible,
could have been 59,853 or 61,142 for the first example, and it could have been 2,78,955
or 2,80,984 for the second example. Imagine and write about, what could have been
the exact number for the third example given above? Similarly, there are many more
possible numbers. Thus,

● to get a rough idea we need estimation.

● to get the estimated value, we generally round off
the numbers to their nearest tens, hundreds or thousands.

Some real life situations where we use estimates
are

(a) Cost of a Television,
Refrigerator, Mixer Grinder etc., is usually expressed in thousands of rupees.

(b) The Voters population
in an Assembly Constituency in a state is often stated in lakhs.

(c) The Central or State Government’s Annual Budget
is usually given in lakh crore.

When an exact answer is not necessary, estimation
strategies can be used to determine a reasonably close answer.

**Activity**

1. Fill
up the jar with some items like Tamarind seeds. Let each student give an estimate
of the number of items. Make a table of the result by finding the difference of
the estimate and the actual amount.

2. Get a large jar and a bag of Tamarind
seeds and put 30 seeds in the jar. Observing the contents, estimate how many seeds
roughly will fill the whole jar. Continue to fill the jar to check your estimate.

Rounding off is one way to find a number for estimation
that is quite convenient. It gives us the closest
suitable number according to a given place value. There are four steps involved
in the rounding process. Let us illustrate this with an example.

__Example 1.11__

Round off the number 8,436 to the nearest hundreds.

__Example 1.12__

Round off the number 78,794 to the nearest thousands.

**Try these**

**● Round off the following numbers to
the nearest ten.**

**(i) 57 (ii) 189 (iii) 3,956 (iv) 57,312**

**Solution:**

(i) 57** **= 7 > 5 → 60

(ii) 189 = 9 > 5 → 190

(iii) 3,956 = 6
> 5 → 3,960

(iv) 57,312 = 2
< 5 → 57,310

**● Round off the following numbers to
the nearest ten, hundred and thousand.**

**(i) 9,34,678 (ii) 73,43,489 (iii) 17,98,45,673**

**Solution: **

**Nearest ten **

(i) 9,34,6__7__8 = 8 > 5 −> 9,34,680

(ii) 73,43,4__8__9 = 9 > 5 −> 73,43,490

(iii) 17,98,45,6__7__3 = 3 < 5 −> 17,98,45,670

**Nearest hundred **

(i) 9,34,__6__78 = 7 > 5 −> 9,34,700

(ii) 73,43,__4__89 = 8 > 5 −> 73,43,500

(iii) 17,98,45,__6__73 = 7 > 5 −> 17,98,45,700

**Nearest thousand **

(i) 9,3__4__,678 = 6 > 5 −> 9,35,000

(ii) 73,4__3__,489 = 4
< 5 −> 73,43,000

(iii) 17,98,45,__6__73
= 6 > 5 −> 17,98,46,000

**● The tallest mountain in the world
Mount Everest, located in Nepal is 8,848
m high.**

**Its height can be rounded to the nearest
thousand as __________.**

**Answer:** **9000**

** **

__1. Estimation of Sum and Difference__

__Example 1.13__

The amount deposited by a Gold merchant in his bank
account in the month of January is ₹17,53,740 and in the month of February is ₹15,34,300.
Estimate the sum and difference of the amount deposited to the nearest thousand.

**Solution**

Rounding off to the nearest thousand is as follows.

**Think**

Is 2,19,340 is rounded off to its nearest thousand as 2,20,000. Why?

**No.
**Round off value : 2,19,000

** **

__2. Estimation of Product and Quotient__

__Example 1.14__

If the cost of a copy
of a Thirukkural book is ₹ 188,
then find the estimated cost of 31 copies of such books. (Note: Find the rounded
values of 188 and 31 and then find the result)

**Solution**

Here, 188 is nearer to 200 and 31 is nearer to 30.

The exact cost of 31 copies is 188 × 31 = ₹ 5828 whereas,

The estimated cost of 31 copies = 200 × 30 = ₹ 6000

Therefore, the estimated cost of 31 copies of Thirukkural
books is ₹ 6000.

__Example 1.15__

Find the estimated value of 5598 ÷ 689.

**Solution**

5600 is nearest to 5598

700 is nearest to 689

Hence, the estimated value of 5598 ÷ 689 is 8

**Try these**

**● Estimate
the sum and the difference : 8457 and 4573.**

**Solution:**

Actual sum = 8457

= 4573

__13030__

8457 + 4573 = 13030

Estimate sum =
8000

(Nearest to thousand) = 5000

__13000__

Hence the estimated sum of 8457 + 4573 = 13,000

Actual difference : 8457 − 4573 = ?

8457

4573

__3884__

8457 − 4573 = 3884

Estimated difference = 8000 − 5000

(Nearest to thousand) = 3000

Hence the estimated difference between 8457 and 4573 is 3000.

**● Estimate
the product: 39 × 53**

**Solution:**

39 × 53 = 2067

Estimated product = 40 × 50

(Nearest to ten) = 2000

Hence the estimated value of 39 × 53 = 2000

**● Estimate the quotient: 5546 ÷ 524**

**Solution:**

Hence Estimated quotient of 5546 ÷ 524 = 11

Tags : Numbers | Term 1 Chapter 1 | 6th Maths , 6th Maths : Term 1 Unit 1 : Numbers

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6th Maths : Term 1 Unit 1 : Numbers : Estimation of numbers | Numbers | Term 1 Chapter 1 | 6th Maths

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