# Worksheet on Estimation and Approximation | Estimating and Rounding Worksheet with Answers

The estimation of Numbers is an integral aspect of mathematics, and we engage in its day-to-day life, approximate value is not good enough occasionally, so we need to know the exact number. 6th Grade Math Students can enhance their math skills by answering the questions from the Estimation Worksheets PDF. Whereas for quick calculation use estimation.

To estimate Sum, Difference, Product, and or Quotient, first, we need to round off the given number to the nearest tens, hundreds, thousand, million, or any other ten multiple numbers, after doing so we need to apply the required mathematical operations. With the help of the Worksheet on Estimation, you can better understand the principles of Estimation. Exercise the Problems in Estimation Worksheet PDF carefully and answer problems fastly in your tests.

Problem 1:
Estimate the following values to the nearest ten,
(i) 36+53
(ii) 57- 43

Solution:

The values are given in the question,
Now, we should round off numbers to the nearest ten multiple.
(i) 36 + 53
First, we have to round off 36 to the nearest 10.
In 36, the units digit is 6, which is greater than 5. So, we have to replace zero in the units place and the tens place digit is increased by one.
So, the 36 is rounded off to 40.
Next, the number is 53. In this unit’s place digit, 3 is less than 5, so we need to replace zero in units digit and keep the remaining digits as it is.
The value 53 is rounded off to 50.
Now, find the estimated sum value.
The sum value is 40 + 50 = 90.
Therefore, the sum of the given value is 90.

(ii)57 – 43
Now, we need to find the difference value.
The value 57 is between 50 and 60, compared to 50, 57 is near to 60. So, the value 57 is rounded off to 60.
Next, the value 43 is between 40 and 50, compared to 50, the value 43 is near to 40. So, 43 is rounded off to 40.
After, perform the subtraction operation, the difference value is,
60 – 40 = 20.
Thus, the final difference value is 20.

Problem 2:
Estimate the following to nearest tens,
(i) 64÷6
(ii) 23 x 82

Solution:

As given in the question the values.
Now, estimate the given numbers to the nearest tens.
(i) 64÷6
Given the value is 64 and 6.
Now, we have to find the estimating quotient value.
First, round off 64 to the nearest 10 which is 60.
Now, divide 60 by 6.
So, the value is
60 ÷ 6 = 10
Therefore, estimating the quotient of given numbers is 60.

(ii) 23 x 82
The number 23 is between 20 and 30. But the value 23 is near to 20 compared to 30. Therefore, 23 is rounded down to 20.
Next, the number 82 is between 80 and 90. But the value 82 is near 80 compared to 90. Therefore, 82 is rounded up to 80.
Now, Multiply 20 and 80.
20 × 80 = 1600.
Hence, the estimated product value is 1600.

Problem 3:
Using the Estimation, find the value to the nearest hundreds. The value is 469+ 972

Solution:

Given the values in the question.
Now, we should round off numbers to the nearest hundreds.
(i) 469 + 972
Now, first, we have to round off 469 to the nearest 100.
In 469, the tens place digit is 6, which is greater than 5. So, we have to replace zero in the units place, tens place, and the hundreds place digit is increased by one.
So, the 469 is rounded off to 500.
Next, the number is 972. In this tens place digit is 7, which is greater than 5. So we need to replace zero in units place digit, tens place digit and increase hundred place digits by one.
The value 972 is rounded off to 1000.
Now, find the estimated sum value.
The sum value is 1000+ 500 = 1500.
Therefore, the sum of the given value is 1500.

Problem 4:
Find the estimation difference value of 826- 421 to the nearest hundred?

Solution:

The given values are 826, and 421.
Now, we need to find the difference value using the estimation.
The value 826 is between 800 and 900, compared to 900, 826 is near to 800. So, the value 826 is rounded off to 800.
Next, the value 421 is between 400 and 500, compared to 500, the value 421 is near to 400. So, 421 is rounded off to 400.
After, perform the subtraction operation, the difference value is,
800 – 400 = 400.
Thus, the final difference value of the given numbers is 400.

Problem 5:
What is the product value of 1678, 3021 to nearest 1000 using the estimation?

Solution:

As given in the question the values.
Now, we need to find the product value to the nearest 1000’s.
First, the number is 1678 is rounded off to 2000.
Next, the number is 3021, which is rounded off to 3000.
Now, perform the multiplication operation.
The product value is,
2000 x 3000 = 60,00,000
Hence, the estimated product value to the nearest 1000 is 60,00,000.

Problem 6:
Using estimation, Find the nearest 100 quotient value of 4210 divided by 3?

Solution:

As given in the question, the values are 4210, and 3.
We have to round off the values and find the quotient value.
The value 4210 is rounded off to 4200, and the dividend value is 3.
Now, divide 4200 by 3.
So, the value is
4200 ÷ 3 = 1400
Therefore, after estimating the quotient of given numbers is 1400.

Problem 7:
Sunny spent 876/- on groceries and 582/- on shopping. While discussing the expenditure he says that she approximately spent 880/- on groceries and 580 on shopping. What is the estimated sum of his expenditure?

Solution:

The data is given in the question.
Now, we need to find the estimated sum of his expenditure.
The Actual expenditure on groceries is 876.
876 can be rounded off to 880.
Next, the Actual expenditure on shopping is 582.
582 can be rounded off to 580.
Now, we can easily find the estimated sum value.
So, the sum is, 880 + 580 = 1460.
Thus, the estimated sum value is 1460.

Problem 8:
Estimate the products of 23 and 76?

Solution:

As, given in the question the values are 23, 76.
Now, we have to estimate the given numbers to the nearest tens, hundreds, or thousands.
The number 23 is between 20 and 30. But the 23 is near to 20 compared to 30. Therefore, 23 is rounded off to 20.
Next, the number 66 is between 60 and 70. But the 66 is near to 70 compared to 60. Therefore, 66 is rounded up to 70.
So, Multiply 20 and 70.
20 × 70 = 1400.
Hence, the estimated product value is 1400.

Problem 9:
Estimate the sum of three digits to the nearest 100. The values are 321 + 216 + 458?

Solution:

The given values are 321, 216, and 458.
Now, we will find the estimated sum value of these numbers.
First, we need to round off the numbers to the nearest 100.
The number 321 tens place digit is 2, which is less than 5. So replace zero in units place digit, and tens place digit, keep the remaining digits as it is.
Next, the number is 216, in this tens place digit is 1, which is less than 5. So replace zero in units place digit, tens place digit, and keep the remaining digit as it is.
In 458, the tens place digit is 5, which is equal to 5. So, replace zero in units place digit, tens place digit, and increase hundreds place digit by one.
After round off, the values are 300, 200, 500.
Now, to perform the addition operation, we get the estimated sum value.
300 + 200 + 500 = 1000
Thus, the estimated sum of the three-digit value is 1000.

Problem 10:
Estimate the product of 482 × 826 to the nearest 10. Write the value.

Solution:

Given the numbers are 482 and 826.
Now, we will estimate the given numbers to the nearest tens, hundreds, and thousands.
The number 482 is between 480 and 490. But the 482 is near to 480 compared to 490. Therefore, 482 is rounded down to 480.
Next, the number 826 is between 820 and 830. But the number 826 is near to 830 compared to 820. Therefore, 826 is rounded up to 830.
Now, Multiply 480 and 830.
480 × 830 = 3,98,400
Therefore, the estimated product value is 3,98,400.