Estimating Numbers
Number estimation is an important aspect of mathematics that we use every day. Whether it’s estimating a bill, a person’s weight, or while solving a math problem. However, sometimes an estimate isn’t enough for a math operation, and we will need to know the exact number.
We will look at two methods of estimating numbers, and then perform addition and subtraction operations.
What is Estimation?
To make calculations easier and more realistic, an estimate of a number is a reasonable guess of the actual value.
Approximating a quantity to the required or nearest accurate value is what estimation is all about.
This is obtained by rounding off the numbers in the calculation and obtaining a quick and approximate answer. A number can be estimated by two methods:
- Rounding off
- Use of compatible numbers
Estimating by Rounding
To round a number, find the rounding digit, or the digit that occupies the place value you want to round to. Then look at the digit to the right of the rounding digit.
- If the number is less than 5, the rounding digit should be left unchanged. And next, we replace the remaining digits to the right with zero.
- If the number is greater than five, increase the rounding digit by one.
- If the number is five, always round up (add one to the rounding digit).
When rounding off a number that is exactly between two other numbers, this rule was created to “break the tie.” These rules are known as “conventions,” and they are necessary so that we all get the same answer when solving the same problems.
As an example let’s look at rounding off the number 16,745.2583 to the thousandth decimal place.
Find the rounding digit first. This is the number “8.” You want the result to be as accurate as possible, so you’re trying to get rid of all the digits to the right of the digit 8.
Now shifting focus to the digit in the ten-thousandths place, which is “3“. Because 3 is less than 5, leave the number “8” as it is and remove the digits to its right. This results in 16,745.258.
In the next example, we round off 14769.3352 to the nearest hundreds.
The digit at the hundreds place is 7, so, the rounding digit is 7. Look at the digit “6” one place to the right of 7. Because 6 is greater than 5, the number must be rounded up. Change all the digits to the right of the rounding digit to zero. You can also get rid of the decimal point. The final number is 14,800.
Let’s find the sum of numbers using the method of estimation by rounding off. The addition equation is: 332.6 + 287.4
By applying the rounding off method, each number should be rounded to the nearest tens. Then we calculate the sum of the rounded numbers.
332.6 rounded to the nearest tens is equal to 330.
And 287.4 rounded to the nearest tens is equal to 290.
Thus, 332.6 + 287.4 equals about 620.
Let’s now find the difference of two numbers by using the estimation by rounding method. The subtraction equation is: 432.6 – 187.4
As seen before in addition, we apply the rounding method so that each number is rounded off to the nearest tens. Then we calculate the difference between the rounded numbers.
432.6 rounded to the nearest tens is equal to 430.
And 187.4 rounded to the nearest tens is equal to 190.
Thus, 432.6 – 187.4 equals about 240.
What is a Compatible Number?
Compatible numbers are those that are simple to mentally add, subtract, multiply or divide. Compatible numbers are similar in value to actual numbers, making it easier to estimate the answer and solve problems.
To make numbers compatible, we can round them up to the nearest ten, hundred, thousand, or ten thousand.
For example, if we need to add 493 and 549, we can round these numbers up to the nearest tens or hundreds to make them compatible. It’s much easier to add 490 and 550 (rounded to the nearest tens) or 500 and 500 (rounded to the nearest hundreds).
Hence, the required answer is about 490 + 550 or 500 + 500 that equals 1040 or 1000, respectively.
Let’s attempt to find the sum using compatible numbers. The numbers and their sum is: 513 + 299 = 812
We can see that 513 and 299 cannot be added easily because they’re incompatible. So, we round both numbers to the nearest tens to make them compatible.
We can also find the difference using compatible numbers. The numbers and the actual difference is: 612.2 – 376.5 = 235.7
We can’t easily tell the difference between 376.5 and 612.2 because they’re incompatible. So, we round both numbers to the nearest tens to make them compatible.
Solved Examples
Example 1:
Find the sum of the numbers 234.6 and 185.3.
Solution:
Method 1:
Applying the rounding method, we need to first round each number to the nearest tens. Then we calculate the sum of the rounded numbers.
Thus, 234.6 + 185.3 is about 420.
Method 2:
Applying the compatible numbers method:
Thus, 234.6 + 185.3 equals about 450.
Example 2:
Find the difference between the numbers 834.6 and 385.3
Solution:
Method 1:
Applying the rounding method, we round each number to the nearest tens. We then calculate the difference between the rounded numbers.
Thus, 834.6 – 385.3 is about 440.
Method 2:
Apply compatible numbers method:
Thus, 834.6 – 385.3 is about 450.
Example 3:
The math book for Class IV has 216 pages and the English book has 196 pages. Calculate the difference in the number of pages between these two books.
Solution:
Apply the rounding method. Each number should be rounded to the nearest tens. Then calculate the difference between the rounded numbers.
216 rounded to the nearest tens is equal to 220.
And 196 rounded to the nearest tens is equal to 200.
Thus,220 – 200 equals 20.
Hence, the difference in the number of pages between the two books is about 20 pages.
Example 4:
A school has 476 female students and 625 male students. Calculate the total number of students enrolled in the school.
Solution:
As usual we apply the rounding method. Each number should be rounded to the nearest tens. Then the difference is calculated between the rounded numbers.
476 rounded to the nearest tens is equal to 480.
And 625 rounded to the nearest tens is equal to 630.
Hence, there are about 1,110 students in the school.
Example 5:
In a watermelon eating contest, Ellie consumed 3.45 pounds of watermelon. Lisa consumed 2.13 pounds of watermelon. What’s the difference between the quantity of watermelon that each of the girls consumed?
Solution:
Apply the rounding method. Each number needs to be rounded to the nearest ones. Then as done before we calculate the difference between the rounded numbers.
3.54 rounded to the nearest ones is equal to 4.
And 2.13 rounded to the nearest ones is equal to 2.
By taking the difference, 4 – 2 = 2.
As a result, Lisa consumed about 2 pounds less than Ellie.
The closest rounded-off value to the exact value is used as an estimate of a particular number.
Estimation saves time and allows us to get a quicker result in a calculation.