TET Syllabus - Mathematics Study Materials in Number System (Part IV)

 

                  Teachers Eligibility Test - Paper 2

 

Class – VI Mathematics

 

                                       NUMBER SYSTEM

                          

ESTIMATION OF NUMBERS                         

                       

                        Nearly 60,000 people watched the Republic day parade at Raj path, 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.

 

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.

                        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

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

Step	To do	8,436 to hundreds
Step 1	Find the digit in hundreds place	8,436
Step 2	Look at the digit to its right	8,436
Step 3	If this digit is 5 or greater, add 1 to it. If it is less than 5, leave it unchanged	8,436 (3<5) Leave 4 unchanged
Step 4	Change the digits to the right of 4 to zeros	8,400

 

 

Example: 2

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

Step	To do	78,794 to thousands
Step 1	Find the digit in thousands place	78,794
Step 2	Look at the digit to its right	78,794
Step 3	If this digit is 5 or greater, add 1 to it. If it is less than 5, leave it unchanged	78,794 (7>5) Add 1 to 8 and Change 8 to 9
Step 4	Change the digits to the right of 79 to zeros	79,000

 

 

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.

 

	Actual Amount	Estimated Amount
Amount deposited in January	17,53,740	17,54,000
Amount deposited in February	15,34,400	15,34,000
Total amount deposited	32,88,140	32,88,000
Difference between the amounts deposited	2,19,340	2,20,000

 

Estimation of Product and Quotient

Example 1.14

If the cost of a copy of a Thirukural 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 8074 + 4178.

Solution:

8100 is nearest to 8074    4200 is nearest to 4178

Actual value

         8074 + 4178 = 12252                                       

Estimated value

          8100 + 4200 = 12300