Estimate Sums

Concept

Estimation of a number is a reasonable guess of the actual value to make calculations easier and realistic. This is obtained by rounding off the numbers involved in the calculation and getting a quick and rough answer. Sometimes we when we add two big numbers, we don’t really want to know the exact sum. We just want to find a quick estimate. We can quickly estimate a sum by rounding each of the addends and adding them together.

Rules

To get an estimate of the sum, round off all the numbers to the same place value, then add them.

How to Round Numbers
There are some basic rules that need to be followed for rounding numbers.
When rounding a number, you first need to ask: what are you rounding it to? Numbers can be rounded to the nearest ten, the nearest hundred, the nearest thousand, and so on.

We first need to know what our rounding digit is. This digit is the one that will ultimately be affected.
After this, we need to check the digit to the right of this place which will decide the fate of the rounding digit.
If the number you are rounding is followed by 0, 1, 2, 3, or 4, we do not change the rounding digit. However, all the digits to the right of the rounding digit are changed to 0.
If the number you are rounding is followed by 5, 6, 7, 8, or 9, we increase the rounding digit by 1, and all the digits to the right of the rounding digit are changed to 0.

Rounding Numbers to the Nearest Ten
Rounding numbers to the nearest ten means we need to check the digit to the right of the tens place, that is the ones place. For example, when we round the number 3186 to the nearest ten, it becomes 3190.

Rounding Numbers to the Nearest Hundred
Rounding numbers to the nearest hundred means we need to check the digit to the right of the hundreds place, that is, the tens place. For example, when 8453 is rounded to the nearest hundred, it becomes 8500.

Example

Estimate 86 + 23.

Solution

To get an estimate of the sum, round off all the numbers to the same place value, then add them.

86 (Round to the nearest 10) → 90

23 (Round to the nearest 10) → 20

Estimated Sum:
90 + 20 = 110

Practice Estimate Sums

Practice Problem 1

Estimate 913 + 756.
Round both numbers to the nearest hundred and then add.

Practice Problem 2

Estimate 32 + 29.
Round both numbers to the nearest ten and then add.

Practice Problem 3

Estimate the sum by rounding each number to the nearest thousand.

Practice Problem 4

A meat shop sold 18,606 kilograms of beef and 35,217 kilograms of mutton in a year. About how many kilograms of meat were sold in total?
Round both numbers to the nearest thousand and then add.