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
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