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Rounding Whole Numbers
In CBSE Board the whole numbers are rounded up for tens, hundreds and thousands.
| Number | thousand | hundred | tens | Ones | ||
| 4123 | 4000 | 100 | 20 | 3 | ||
| Number of Digits |
4 digits | 3 digits | 2 digits | 1 digit | ||
| Number of digits to be Rounded in | 4 -1 = 3 digits | 3-1 = 2 digits | 2-1 =1 digit | 1-1 = 0 digit | ||
Now suppose you have a number as shown above 4123 and you want to round up to thousand' value then as shown in table we have to round 3 digits. That is
4123 - 123( 3 digits) = 4000 Minimum Value for Thousand Number
4000 (Minimum Value obtained above) + 1000 (indicates thousand number) = 5000 (Maximum Value for Thousand Number
<|----------|---------------------------|---------------------------------------------------|>
4000 4123 4500 5000
4123 is less than 4500 so we round 4123 to 4000. So 4000 is the number rounded up for thousand number
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Suppose you want to round up hundred value then you have to round up 3-1 = 2 digits so we get
123 - 23 = 100 (Minimum Value for Hundred Number
100 ( Minimum Value obtained above) + 100 (indicates hundred number) = 200 (Maximum value for hundred number)
<|----------|---------------------------|---------------------------------------------------|>
100 123 150 200
123 is less than 150 so we round 123 to 100. So 100 is the number rounded up for hundred number
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Suppose you want to round up tens value then you have to round up 2-1 = 1 digits so we get
23 - 3 = 20 (Minimum Value for tens Number
20 ( Minimum Value obtained above) + 10 (indicates tens number) = 30 (Maximum value for hundred number)
<|----------|---------------------------|---------------------------------------------------|>
20 23 25 30
23 is less than 25 so we round 23 to 20. So 20 is the number rounded up for tens number
Note 4500 (thousand number), 150 (hundred number), 25 (tens number) are midpoint values and you have to see whether the number is on left hand side of mid point or right hand side of mid point and based on that you round up the number. If the number is greater then mid point then the rounded value would be maximum value obtained as shown above. For eg for rounding thousand number if the value is 4723 then rounded value would be 5000.
ESTIMATION IN SUMMATION, SUBTRACTION AND MULTIPLICATION: (DIVISION IS NOT INCLUDED IN BOOK)
The method shown below is applicable to all the three i.e. for summation, subtraction and multiplication.
SUMMATION AND SUBTRACTION ESTIMATION:
1) SUM 1:
23 + 105
23 - has 2 digits
105 - has 3 digits.
23 is tens and 105 is hundreds.
In Summation and Subtraction you round up upto smallest number in the sum. For eg 23 is smaller then 105 therefore round up 23 which is tens and round up 105 also as tens and not as hundreds.
Therefore:
23 - rounding up will give 20
and 105 rounded up as tens will give 110.
Adding the two rounded number will give:
20 + 110 = 130.
The Actual Answer is 23 + 105 = 128 therefore estimate is very close to the actual number.
SUBTRACTION:
Taking the same sum 23 and 105 i.e. 105 - 23 = ?
As rounded above we get 105 = 110 and for 23 we get 20.
110 - 20 = 90
Correct Value = 105 - 23 = 82 which is very close to our estimate of 90.
Now suppose you have to numbers 45 and 215. In multiplication we round up individual numbers separately. So we round up 45 as tens and 215 as hundreds.
So rounding 45 we get 50
Rounding up 215 which is hundreds we get = 200
Multiplication of 50 x 200 = 10000
Actual Answer = 45 x 215 which is = 9675
This answer is close to 10,000 which we estimated above.
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