Q: Round off the given numbers to the nearest tens, hundreds and thousands.

\$75847\$ - Nearest Ten: \$75850\$\$75847\$ - Nearest Hundred: \$75800\$\$75847\$ - Nearest Thousand: \$76000\$\$75847\$ - Nearest Ten Thousand: \$80000\$.

Q: Round these numbers to the nearest tens.\$28, 32, 52, 41, 39, 48, 64, 59, 99, 215, 1453, 2936\$.

\$28=30\$\$32=30\$\$52=50\$\$41=40\$\$39=40\$\$48=50\$\$64=60\$\$59=60\$\$99=100\$\$215=220\$\$1453=1450\$\$2936=2940\$.

Q: Estimate the product \$475\times 225\$ rounding off each number to the nearest hundred.

In \$475\$ the last two digits i.e., \$75\$ is greater than \$50\$.Therefore, \$1\$ will be added to the 3rd last digit and the last two digits will become zero.After rounding to nearest hundred we will get \$500\$.In \$225\$ the last two digit i.e., \$25\$ is less than \$50\$Thus, the 3rd last will remain same and the last digit will become zero.After rounding to nearest ten we will get \$200\$.Hence, the required product is \$500\times 200 = 1,00,000\$

Q: Subtract: \$3xy + 5yz- 7zx\$ from \$5xy -2yz- 2zx + 10xyz\$

Subtract \$3xy + 5yz-7zx\$ from\$5xy - 2yz - 2zx + 10xyz\$ \$5xy - 2yz - 2zx + 10xyz-(3xy + 5yz-7zx)\$\$=5xy - 2yz - 2zx + 10xyz-3xy - 5yz+7zx\$\$=2xy-7yz+5zx+10xyz\$

Q: Solve : \$2a - [4b - \{4a - (3b - \overline{2a + 2b})\}]\$

\$2a−[4b−{4a−(3b−\bar{2a+2b})}]\$\$2a−[4b−{4a−(3b−2(a+b))}]\$\$2a−[4b−{4a−(3b−2a-2b)}]\$\$2a−[4b−{4a−(b−2a)}]\$\$2a−[4b−{4a−b+2a)}]\$\$2a−[4b−{6a−b)}]\$\$2a−[4b−6a+b]\$\$2a−[5b−6a]\$\$2a−5b+6a\$\$8a−5b\$

Q: Estimate the sum \$(42505+27807+21397)\$ to the nearest thousand.

\$42505\$ estimated to the nearest thousand \$= 43000\$\$27807\$ estimated to the nearest thousand \$= 28000\$\$21397\$ estimated to the nearest thousand \$= 21000\$Now, the sum of the estimated numbers is \$43000+28000+21000=92000\$Hence, the sum is \$92000\$.

Q: Estimate the sum to the nearest ten:\$(57 + 34)\$

Estimated value to the nearest ten of \$57 = 60\$Estimated value to the nearest ten of \$34 = 30\$Total required estimation \$= ( 60 + 30) = 90\$

Q: Round-off \$3789\$ to nearest \$100\$

\$\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\$

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

\$\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.\$

Question 1

Round off the given numbers to the nearest tens, hundreds and thousands.

Accepted Answer

$75847$ - Nearest Ten: $75850$$75847$ - Nearest Hundred: $75800$$75847$ - Nearest Thousand: $76000$$75847$ - Nearest Ten Thousand: $80000$.

Question 2

Round these numbers to the nearest tens.$28, 32, 52, 41, 39, 48, 64, 59, 99, 215, 1453, 2936$.

Accepted Answer

$28=30$$32=30$$52=50$$41=40$$39=40$$48=50$$64=60$$59=60$$99=100$$215=220$$1453=1450$$2936=2940$.

Question 3

Round off to nearest lakhs: The given number is $38,65,62,048$

Accepted Answer

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 $38,66,00,000$

Question 4

Estimate the product $475\times 225$ rounding off each number to the nearest hundred.

Accepted Answer

In $475$ the last two digits i.e., $75$ is greater than $50$.Therefore, $1$ will be added to the 3rd last digit and the last two digits will become zero.After rounding to nearest hundred we will get $500$.In $225$ the last two digit i.e., $25$ is less than $50$Thus, the 3rd last will remain same and the last digit will become zero.After rounding to nearest ten we will get $200$.Hence, the required product is $500\times 200 = 1,00,000$

Question 5

Subtract: $3xy + 5yz- 7zx$ from $5xy -2yz-  2zx + 10xyz$

Accepted Answer

Subtract $3xy + 5yz-7zx$ from$5xy - 2yz - 2zx + 10xyz$  $5xy - 2yz - 2zx + 10xyz-(3xy + 5yz-7zx)$$=5xy - 2yz - 2zx + 10xyz-3xy - 5yz+7zx$$=2xy-7yz+5zx+10xyz$

Question 6

Solve : $2a - [4b - \{4a - (3b - \overline{2a + 2b})\}]$

Accepted Answer

$2a&#8722;[4b&#8722;{4a&#8722;(3b&#8722;\bar{2a+2b})}]$$2a&#8722;[4b&#8722;{4a&#8722;(3b&#8722;2(a+b))}]$$2a&#8722;[4b&#8722;{4a&#8722;(3b&#8722;2a-2b)}]$$2a&#8722;[4b&#8722;{4a&#8722;(b&#8722;2a)}]$$2a&#8722;[4b&#8722;{4a&#8722;b+2a)}]$$2a&#8722;[4b&#8722;{6a&#8722;b)}]$$2a&#8722;[4b&#8722;6a+b]$$2a&#8722;[5b&#8722;6a]$$2a&#8722;5b+6a$$8a&#8722;5b$

Question 7

Estimate the sum $(42505+27807+21397)$ to the nearest thousand.

Accepted Answer

$42505$ estimated to the nearest thousand $= 43000$$27807$ estimated to the nearest thousand $= 28000$$21397$ estimated to the nearest thousand $= 21000$Now, the sum of the estimated numbers is $43000+28000+21000=92000$Hence, the sum is $92000$.

Question 8

Estimate the sum to the nearest ten:$(57 + 34)$

Accepted Answer

Estimated value to the nearest ten of $57 = 60$Estimated value to the nearest ten of $34 = 30$Total required estimation $= ( 60 + 30) = 90$

Question 9

Round-off $3789$ to nearest $100$

Accepted Answer

$\Rightarrow$  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 $3800$

Question 10

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

Accepted Answer

$\Rightarrow$  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 $1290,\,1300,\,1000.$

Revise with Concepts

Estimating and Rounding Off

Estimating the Results of Operations

Quick Summary With Stories

Estimating to the nearest tens by rounding off

Estimating to the nearest hundreds by rounding off

Estimating to nearest Thousand by rounding Off

Estimating the Results of Operations-I

Estimating the Results of Operations-II

Round off the given numbers to the nearest tens, hundreds and thousands.

Round these numbers to the nearest tens.
$28, 32, 52, 41, 39, 48, 64, 59, 99, 215, 1453, 2936$ .

Round off to nearest lakhs: The given number is $38, 65, 62, 048$

Estimate the product $475 \times 225$ rounding off each number to the nearest hundred.

Subtract:
$3 x y + 5 y z - 7 z x$ from $5 x y - 2 y z - 2 z x + 10 x y z$

Solve : $2 a - [4 b - {4 a - (3 b - \overline{2 a + 2 b})}]$

Estimate the sum $(42505 + 27807 + 21397)$ to the nearest thousand.

Estimate the sum to the nearest ten:
$(57 + 34)$

Round-off $3789$ to nearest $100$

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

Revise with Concepts

Estimating and Rounding Off

Estimating the Results of Operations

Quick Summary With Stories

Estimating to the nearest tens by rounding off

Estimating to the nearest hundreds by rounding off

Estimating to nearest Thousand by rounding Off

Estimating the Results of Operations-I

Estimating the Results of Operations-II

Round off the given numbers to the nearest tens, hundreds and thousands.

Round these numbers to the nearest tens. 28,32,52,41,39,48,64,59,99,215,1453,2936.

Round off to nearest lakhs: The given number is 38,65,62,048

Estimate the product 475×225 rounding off each number to the nearest hundred.

Subtract: 3xy+5yz−7zx from 5xy−2yz−2zx+10xyz

Solve : 2a−[4b−{4a−(3b−2a+2b​)}]

Estimate the sum (42505+27807+21397) to the nearest thousand.

Estimate the sum to the nearest ten: (57+34)

Round-off 3789 to nearest 100

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

Round these numbers to the nearest tens.
$28, 32, 52, 41, 39, 48, 64, 59, 99, 215, 1453, 2936$ .

Round off to nearest lakhs: The given number is $38, 65, 62, 048$

Estimate the product $475 \times 225$ rounding off each number to the nearest hundred.

Subtract:
$3 x y + 5 y z - 7 z x$ from $5 x y - 2 y z - 2 z x + 10 x y z$

Solve : $2 a - [4 b - {4 a - (3 b - \overline{2 a + 2 b})}]$

Estimate the sum $(42505 + 27807 + 21397)$ to the nearest thousand.

Estimate the sum to the nearest ten:
$(57 + 34)$

Round-off $3789$ to nearest $100$

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