Estimating the Results of Operations

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

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\$

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.\$