Estimation of Numbers

Every single day of our living, we are always estimating and that is unconscious. Have you seen your parents use weighing machines while they are cooking? Not really. They usually estimate what has to go into the dish and how much has to go into the dish. Let’s say you and your sibling are sharing a bar of chocolate. You estimate when your sibling gets the right mount by comparing both the pieces or consider a stock analyst. They usually estimate the trends in the or determine them. If estimation has to be described, then estimation is to form an appropriate judgement about something’s worth, amount, weight, size, etc. Or in other simpler words, you calculate anything approximately. 


Estimation of Numbers By Rounding Off Method

In Mathematics, even before we manually solve the problem or even put it down on a paper, we tend to calculate the result in our heads. And we don’t usually calculate the exact value, we calculate the approximate value or we round it off to the nearest whole number. In Mathematics, rounding off is used quite often to estimate the value of an object. There are rules to be followed when you have to round off a digit to a whole number. You have to see the number to the right of the digit. Next, if the number is equal to or more than 5, then you round off the digit to the next number. If the number is less than 5, then you round off the digit to the same number. Let us say that you need to round off 7.8. Now, the number next to 7 is 8. 8 is a number that is greater than 5. Hence, 7 will be rounded off to 8. The estimate number here is 8.


Uses of Estimation of Numbers

Estimation is to form an appropriate judgement about something’s worth, amount, weight, size, etc. Or in other simpler words, you calculate anything approximately. This is done in order to above the complexity of calculations. Now, there is a major difference between the word exact and the word estimation. The word exact means equal quantity and estimation means something close to the actual value. Estimation is known to save you a lot of time. But when you round off the values, you don’t even need calculators to find the required solution of a given problem. But in Mathematics, you need to get an exact answer and not an estimated answer. Hence, you use it to find the number which is close enough to the solution. 


Solved Examples

Question 1: Round off the following numbers to the nearest whole number.

  1. 3.6

  2. 86.12

  3. 43.85

  4. 23.5423


Solution:  

  1. 3.6

The number next to 3 is 6. The number 6 is more than 5. Hence, you will round off the 3 to the next whole number that is 4. The estimate number here is 4.


  1. 86.12

The number next to 1 is 2. The number 2 is less than 5. Hence, you will retain the same number. Next, the number next to 6 is 1. The number 1 is less than 5. Hence, you will retain the same number. Hence, you will be rounding and estimate by rounding off the 86 to the same whole number that is 86. The estimate by rounding off the number here is 86.


  1. 43.85

The number next to 8 is 5. The number 5 is equal to 5. Hence, you will be rounding and estimating it off to the next number. Next, the number next to 3 is 9. The number 9 is greater than 5. Hence, you will round it off to the next number. Hence, you will be rounding and estimating the 43 to the next whole number, your final answer will be 44. The estimate number here is 44.


  1. 23.5423

The number next to 2 is 3. The number 3 is less than 5. Hence, you will retain the same number. Next, the number next to 4 is 2. The number 2 is less than 5. Hence, you will retain the same number. Next, the number next to 5 is 4.  The number 4 is less than 5. Hence, you will retain the same number. Next, the number next to 3 is 5. The number 5 is equal to 5. Hence, you will round it off to the next number.  Hence, you will be rounding and estimating the number 23 to the next whole number, your final answer will be 24. The estimate by rounding off the number here is 24.

FAQ (Frequently Asked Questions)

1) Explain Rounding and Estimating off of Numbers.

In Mathematics, rounding off is used quite often to estimate by rounding off the value of an object. There are rules to be followed when you have to round off a digit to a whole number. You have to see the number to the right of the digit. Next, if the number is equal to or more than 5, then you round off the digit to the next number.  if the number is less than 5, then you round off the digit to the same number. Let us say that you need to round off 7.8. Now, the number next to 7 is 8. 8 is a number that is greater than 5. Hence, 7 will be rounded off to 8.

2) What is the Difference Between Exact and Estimation?

There is a major difference between the word exact and the word estimation. The word exact means equal quantity and estimation means something close to the actual value. Estimation is known to save you a lot of time. But when you round off the values, you don’t even need calculators to find the required solution of a given problem. But in Mathematics, you need to get an exact answer and not an estimated answer. Hence, you use it to find the number which is close enough to the solution.