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Logical approximation of number - class-VI

Description: logical approximation of number
Number of Questions: 31
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Tags: know the numbers whole numbers mental arithmetic logical approximation of number numbers maths large numbers knowing our numbers place value, ordering and rounding estimation
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Round off to nearest lakhs: The given number is $38,65,62,048$

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $38,68,60,000$

  2. $38,65,600$

  3. $38,65,00,000$

  4. $38,66,00,000$

Show answer
Correct Option: D
Explanation:

To round of the given no in nearest lakh we need to see the value at ten thousand place which is $6$ it is more than $5$. 

So we round off lakhs digit to $5+1=6$
So we will round off. $38,65,62,048$ will become $38,66,00,000$

Round off  $231$ to nearest $100.$

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $200$

  2. $300$

  3. $250$

  4. $350$

Show answer
Correct Option: A
Explanation:

$\Rightarrow$  In number $231$,tens digit is $3$ 

$\Rightarrow$  Its tens digit is 3, which is less than 5. So, we replace each of the tens and ones digits by $0$ and keep the other digits as they are to round off the given number to nearest hundreds.
$\therefore$  Round of 231 to nearest 100 is $200$.

Round off $829$ to nearest $100$. 

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $800$

  2. $700$

  3. $900$

  4. $850$

Show answer
Correct Option: A
Explanation:

$\Rightarrow$  The given number is $829$

$\Rightarrow$  Its tens digit is $2$, which is less than $5$. 
$\Rightarrow$  So, we replace each of the tens and ones digits by $0$ and keep the other digits as they are to round off the given number to nearest $100.$
$\therefore$  Round off $829$ to nearest $100$ is $800$.

Round off $7065$ to nearest $1000$  :

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $700$

  2. $7000$

  3. $70$

  4. $7$

Show answer
Correct Option: B
Explanation:

Rounding off $7065$ to nearest $1000$ we check if $065$ is less than $500$ or not,

As $065 < 500$, we round it off to $000$

$\therefore 7065$ to nearest $1000$ equals $7000$

Round off  $63$ to nearest $10$ 

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $60$

  2. $70$

  3. $65$

  4. $63$

Show answer
Correct Option: A
Explanation:

Rounding off $63$ to nearest $10$ we check if $3$ is less than $5$ or not,

As $3 < 5$, we round it off to $0$

$\therefore 63$ to nearest $10$ equals $60$

Round off the following number to the nearest $10$ and $100$:
$1634$

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $1630,1600$

  2. $1640,1730$

  3. $1740,1700$

  4. $1640,1734$

Show answer
Correct Option: A
Explanation:
$1634=163.4 \times  10^1$

Rounding to nearest 10, we round off $163.4$ to $163.0$ as $4$ is less than $5$

Answer: $1630$

Similarly for 100 th position 
$1634 = 16.34\times 20^2$

$16.34 = 16.30 = 16.00$

So the answer is $1600$.

Round-off $76,890$ to nearest $10$.

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $76,890$

  2. $76,880$

  3. $76,900$

  4. $77,000$

Show answer
Correct Option: A
Explanation:

$\Rightarrow$   The given number is $76,890$.

$\Rightarrow$   In number 76890, its unit digit is $0$, which is already nearest to 10.
$\Rightarrow$  So, don't need to change anything.
$\therefore$   $76,890$ is nearest to 10.

Round-off $4353$ to nearest $100$.

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $4353$

  2. $4350$

  3. $4360$

  4. $4400$

Show answer
Correct Option: D
Explanation:

$\Rightarrow$  The given number is $4353$

$\Rightarrow$  In number 4353, its tens digit is 5, which is equal to 5. 
$\Rightarrow$  So, we increase the digits at hundreds place by 1 and replace each one of the digits at tens and ones place by 0 to round off the given number to nearest to 100.

$\therefore$   The number becomes $4400$

Round-off $52,398$ to nearest $1000$.

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $52,390$

  2. $52,400$

  3. $52,000$

  4. $53,000$

Show answer
Correct Option: C
Explanation:

$\Rightarrow$  The given number is $52,398$

$\Rightarrow$  In number $52398$, its hundred digit is $3$, which is less than $5$. 
$\Rightarrow$  So, we replace each one of the digits at hundreds, tens and ones place by $0$ to round off the given number to nearest to $1000$.

$\therefore$   The number becomes $52,000$

Round-off $3789$ to nearest $100$

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $3789$

  2. $3790$

  3. $3800$

  4. $4000$

Show answer
Correct Option: C
Explanation:

$\Rightarrow$  The given number is $3789$

$\Rightarrow$  In number 3789, its tens digit is 8, which is greater than 5. 
$\Rightarrow$  So, we increase the digits at hundreds place by 1 and replace each one of the digits at tens and ones place by 0 to round off the given number to nearest to 100.

$\therefore$   The number becomes $3800$

Round-off $47,897$ to nearest $1000$.

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $47,897$

  2. $48,000$

  3. $47,900$

  4. $47,890$

Show answer
Correct Option: B
Explanation:

$\Rightarrow$  The given number is $47,897$

$\Rightarrow$  In number 47897, its hundred digit is 8, which is greater than 5. 
$\Rightarrow$  So, we increase the digits at thousand place by 1 and replace each one of the digits at hundreds, tens and ones place by $0$ to round off the given number to nearest to 1000.

$\therefore$   The number becomes $48,000$

Fill in the blanks.
(i) The number 825642 rounded off to nearest thousand is   P  .
(ii) Estimated product of 4023 and 198 is   Q  .
(iii) CXXXI is written in Hindu-Arabic numeral as    R   .
P   Q   R

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. 820000 800000 131

  2. 826000 800000 131

  3. 826000 850000 135

  4. 825000 800000 135

Show answer
Correct Option: B
Explanation:

(i) 825642 rounded off to nearest thousand = 826000
(ii) 4023 estimated to 4000
 198 estimated to 200.
$\therefore$ estimated product = $4000\times 200$ = 800000
(iii) C denoted for 100
     X denotes for 10  
      I denotes for 1
$\therefore$ CXXXI denotes 131

State 'T' for true and 'F' for false.
I. Rounding off $2560$ to the nearest thousand, we get $2000$.
II. Place value of $9$ in $974304200 $ is ninety crore.
Ill. $1$ lakh $= 1000$ thousand
IV. Roman numeral for the smallest four-digit number is $M$.
I  II  III  IV

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. T F T F

  2. F F T T

  3. T T T T

  4. F T F T

Show answer
Correct Option: D
Explanation:

I.Rounding off $2560$ to the nearest thousand, we get $3000$. 

So, I is false
II. Place value of $9$ in $90,00,00,000$. 

So, II is true
III. $1$ lakh $= 1,00,000 = 100 $ thousand
IV. Smallest four digit number $= 1000$
Roman Numeral is $M$.
So, it is true

Estimate the difference of $15875 $ and $7892$ by rounding off each number to nearest hundred.

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $7983$

  2. $8100$

  3. $7900$

  4. $8000$

Show answer
Correct Option: D
Explanation:

$15875$ estimated to nearest hundred is $15900$
$7892 $ estimated to nearest hundred is $7900$
Thherefore, required difference is $15900-7900 =8000$.

What will be the rounded off sum of these figures, $2.303 + 6.66 $ to two decimal point?

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $8.969$

  2. $8.96$

  3. $8.9$

  4. $8.97$

Show answer
Correct Option: B
Explanation:

$2.303+6.66=8.963$


It can rounded off and written as $8.96$ $.$

Mark the correct alternative of the following.
Total number of numbers which when rounded off to nearest ten give us $200$ is?

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $9$

  2. $10$

  3. $8$

  4. $7$

Show answer
Correct Option: B
Explanation:

$195, 196, 197, 198, 199, 200, 201, 202, 203, 204$ are the numbers that when rounded off to nearest ten give us $200$.


Hence, total number of numbers which when rounded off to nearest ten give us $200$ is $10$.

Mark the correct alternative of the following.
The difference between the greatest and smallest numbers which when rounded off a number to the nearest tens as $540$, is?

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $10$

  2. $9$

  3. $8$

  4. $11$

Show answer
Correct Option: B
Explanation:
We know that the greatest number that when rounded off to the nearest tens will become $540 = 544$

Least number that when rounded off to the nearest tens will become $540 = 535$

So, the difference between them $= 544 − 535 = 9$

Hence, the difference between the greatest and smallest numbers which when rounded off a number to the nearest tens as $540$ is $9$.

Mark the correct alternative of the following.
The smallest number which when rounded off to the nearest hundred as $600$, is?

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $550$

  2. $595$

  3. $604$

  4. $599$

Show answer
Correct Option: A
Explanation:

The number from $550$ to $649$ are rounded off nearest hundred as $600$. Therefore, the smallest number is $550$.


Hence, the smallest number which when rounded off to the nearest hundred as $600$ is $550$.

Mark the correct alternative of the following.
The greatest number which when rounded off to the nearest thousand as $7000$, is?

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $6500$

  2. $6549$

  3. $7499$

  4. $6499$

Show answer
Correct Option: C
Explanation:

Numbers from $6500$ to $7499$ are rounded off to nearest thousand as $7000$. Therefore, the greatest number is $7499$.


Hence, the greatest number which when rounded off to the nearest thousand as $7000$ is $7499$.

Mark the correct alternative of the following.
The difference between the greatest and smallest numbers which when rounded off a number to the nearest hundred as $6700$, is?

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $100$

  2. $99$

  3. $98$

  4. $101$

Show answer
Correct Option: B
Explanation:
We know that the greatest number that when rounded off to the nearest hundred will become$ 6,700 = 6749$

Least number that when rounded off to the nearest hundred will become $6,700 = 6650$

So, the difference between them $= 6,749 − 6,650 = 99$

Hence, the difference between the greatest and smallest numbers which when rounded off a number to the nearest hundred as $6700$ is $99$.

Mark the correct alternative of the following.
$2985$ is rounded off to the nearest hundred and the nearest tens. The difference between the two values is?

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $5$

  2. $100$

  3. $10$

  4. $150$

Show answer
Correct Option: C
Explanation:
$2985$ estimated to the nearest hundred $= 3000$

$2985$ estimated to the nearest tens $=2990$

Now, the difference between the nearest hundred and nearest tens of $2985$ is:

$3000-2990=10$

Hence, the difference between the two values is $10$.

Mark the correct alternative of the following.
$1827$ when rounded off to be nearest hundred is?

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $1900$

  2. $1820$

  3. $1850$

  4. $1800$

Show answer
Correct Option: D
Explanation:
Rounding a number to the nearest hundred, we use the following rules:

A) We round the number up to the nearest hundred if the last two digits in the number are $50$ or above.

B) We round the number down to the nearest hundred if the last two digits in the number are $49$ or below.

C) If the last two digits are $00$, then we do not have to do any rounding, because it is already to the hundred.

Now, we are given a number $1827$ whose hundred place is $27$ which is below $50$, therefore, the nearest hundred to $1827$ is $1800$.

Hence, the nearest hundred of $1827$ when rounded off is $1800$.

Round off 11,125 to thousand place

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. 11,000

  2. 12,000

  3. 11,120

  4. 1,100

Show answer
Correct Option: A
Explanation:
The given number is $11,125$. The ones place of the number is $5$, the tens place is $2$, the hundreds place is $1$ and the thousands place is $1$.

Its digit at hundreds place is $1$, which is less than 5. So, we replace each of the hundreds, tens and ones digits by $0$ and keep the other digits as they are.

Therefore, the number $11,125$ is rounded off to nearest thousands as $11,000$.

Hence, the number $11,125$ is rounded off to nearest thousands as $11,000$.

Round off to nearest thousands. The given number is 76,823

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $76,000$

  2. $75,000$

  3. $77,000$

  4. $78,000$

Show answer
Correct Option: C
Explanation:
The given number is $76823$. The one's place of the number is $3$, the tens place is $2$, the hundreds place is $8$ and the thousands place is $6$.

Its digit at hundreds place is $8$, which is greater than $5$. 

So, we increase the digit at thousands place by $1$ and replace each one of the digits at hundreds, tens and ones place by $0$ to get the rounded off numbers that is the number $76823$ is rounded off to nearest thousands as $77000$.

Hence, the number $76823$ is rounded off to the nearest thousands as $77000$.

Round off to nearest thousands. The given number is 24,500

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $24,400$

  2. $24,600$

  3. $25,000$

  4. $24,000$

Show answer
Correct Option: C
Explanation:
The given number is $24,500$. The one's place of the number is $0$, the tens place is $0$, the hundreds place is $5$ and the thousands place is $4$.

Its digit at hundreds place is $5$.

So, we increase the digit at thousands place by $1$ and replace each one of the digits at hundreds, tens and ones place by $0$ to get the rounded off numbers that is the number $24,500$ is rounded off to nearest thousands as $25,000$.

Hence, the number $24,500$ is rounded off to the nearest thousands as $25000$.

Find the product of 5 and the difference between 328 tenths and 4587 thousandths. Round off your answer to 1 decimal place. 

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $146.9$

  2. $141.1$

  3. $139.2$

  4. $140.2$

Show answer
Correct Option: B
Explanation:
Here we want to find a product of $5$ and the difference between $328$ tenths and $4587$ thousandths.

So,
First we find tenth of $328 = \dfrac {328}{10}  =  32.8$
And
Thousandths of $4587  = \dfrac {4587}{1000}  =  4.587$

And difference between them  $=  32.8  - 4.587  = 28.213$

Now product of $5$ and the difference between $328$ tenths and $4587$ thousandths  $=  5\times 28.213  = 141.065$

And we know that if the hundredths places are fifty or more, the tenths place is increased by one.

Hence, round off answer to 1 decimal place is $141.1$

 Round off $690$ to nearest $100$.

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $780$

  2. $690$

  3. $700$

  4. $800$

Show answer
Correct Option: C
Explanation:

$\Rightarrow$  The given number is $690$

$\Rightarrow$  Its tens digit are $9$, which is greater than $5$. 
$\Rightarrow$  So, we increase the digits at hundreds place by $1$ and replace each one of the digits at tens and ones place by $0$ to round off the given number to nearest $100$.
$\therefore$   Round off $690$ to nearest $100$ is $700.$

Round off to the nearest $10, 100,$ and $1000$:
$1289$

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $1290,1389,1009$

  2. $1290,1300,1000$

  3. $1280, 1300, 1200$

  4. $1280,1200,1000$

Show answer
Correct Option: B
Explanation:

$\Rightarrow$  Round off to 10 for 1289 is 1280 or 1290 but nearest to 1289 is 1290.

$\Rightarrow$  So, round off to the nearest $10$ is $1290$.
$\Rightarrow$  Round off to 100 for 1289 is 1200 or 1300 but nearest to 1289 is 1300.
$\Rightarrow$  So, round off to the nearest $100$ is $1300$.

$\Rightarrow$  Round off to 1000 for 1289 is 1000 or 2000 but nearest to 1289 is 1000.
$\Rightarrow$  So, round off to the nearest $1000$ is $1000$.

$\therefore$  The answer is $1290,\,1300,\,1000.$

Round-off $13$ to nearest $10$.

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $10$

  2. $20$

  3. $13$

  4. $1$

Show answer
Correct Option: A
Explanation:

$\Rightarrow$  The given number is $13$

$\Rightarrow$   Its unit digit is $3$ which is less than 5.
$\Rightarrow$   So, we replace unit digit by $0$ keep the other digits as they are to round off the given number to nearest $10$
$\therefore$   Round-off 13 to nearest 10 is $10$.

$(7268 - 2427)$ estimated to the nearest hundred is

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $4800$

  2. $4900$

  3. $4841$

  4. $5000$

Show answer
Correct Option: A
Explanation:

The given value is $7268-2427=4841$

the tens value is $4$ which is less than $5$, so
the estimate value is $4800$.

Rohit's teacher asked him to tell the correct answer after performing the steps given.
$\bullet$ Round off $43, 98$ and $250$ to nearest tens.
$\bullet$ After rounding off, add them.
$\bullet$ Round off the sum to the nearest hundreds.
Then, the correct answer is __________.

maths mental arithmetic estimation and rounding off estimations, bounds and rounding off rounding off numbers rounding of decimals

  1. $300$

  2. $400$

  3. $350$

  4. $480$

Show answer
Correct Option: B
Explanation:

Rounding off to nearest tens:

If unit digit is $0,1,2,3,4$ then round down to nearest tens.
If unit digit is $5,6,7,8,9$ then, round up to nearest tens.
$43$ $\rightarrow$ $40$
$98$ $\rightarrow$ $100$
$250$ $\rightarrow$ $250$
$40+100+250$ $\rightarrow$ $390$
$390$  $\rightarrow$  $400$
Hence, Option B is correct.

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