## Friday

### 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