Tag: estimations, bounds and rounding off

Questions Related to estimations, bounds and rounding off

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 $4800$.