What is an estimate in maths?
Estimation is a term used in maths to change a number to the nearest whole numbers of 10, 100, 1000, 10000 etc. Estimated values are used in making an estimate of something so that a guess can be made. Such value should be a nearest value to the actual value.
The driver of a truck who loads bricks can give estimated value of number of bricks to the supplier about how many bricks he can load in the truck.
If the driver says 1000, then 1000 will be considered as an estimated number of bricks, not the exact. The exact number of bricks eventually be known after the truck loads fully.
The exact and accurate number of bricks can be 1028, which is more than 1000 or it can be 988 which is less than 1000. The driver gives only an estimate so that the supplier at least can know the nearest value of 1000 before filling the truck.
Exact values are always written with sign of equal to (=) and the estimated values are written with sign of approximately equal to (≈)
Another example of estimated values of a number 1256 are 1260 or 1300 or 1000. In this example 1256 is an accurate or exact value, which may belong to some quantity or measurement, but the other values 1260, 1300 and 1000 are called the estimated values of 1256.
Table 1: Estimations of 1256
| Exact value | Nearest to | Estimation value |
|---|---|---|
| = 1256 | 10 | ≈ 1260 |
| = 1256 | 100 | ≈ 1300 |
| = 1256 | 1000 | ≈ 1000 |
Estimations of a whole number are determined by rounding the given number to the nearest values of 10, 100, 1000, 10000,…. and so on. There are steps to round off the whole number. So, what are the rules to estimate? Let’s see next.
Round off to the nearest 10
Rounding off whole numbers to the nearest 10 means to round the digit at ones place.
If the digit at ones place is less than 5, then that digit is changed to 0.
If the digit is equal to or greater than 5, then that digit at the tens place is increased by one and the
digit at ones place is changed to 0.
Keep rest of the digits at other places unchanged.
Example 1: Round 1324 to the nearest 10
The digit at ones place is 4
4 is less than 5. So, the digit 4 will be changed to 0
∴ the rounding of 1324 to its the nearest tens is 1320
Example 2: Round off 39828 to the nearest 10
The digit at ones place is 8, which is greater than 5
So, increase the digit 2 at tens place by 1
which becomes 2 + 1 = 3
Change the digit 8 at ones place to 0
∴ the rounding of 39828 to its the nearest 10 is 39830
Rounding to the nearest 100
In rounding whole numbers to the nearest 100 means the digit at tens place is checked, if it is equal, less
or greater than 5. If tens place digit is equal to or greater than 5, then increase digit at the hundreds place by one.
If it is less than 5, then both digits at the ones and tens places are changed to 0 and there will be no
change in hundreds place.
Example 1: Round 65735 to the nearest 100
The digit at tens place is 3
3 is less than 5. So, 3 at tens place and 5 at ones place will be changed to 0
∴ the rounding of 65735 to the nearest 100 is 65700
Example 2: Round 39457 to the nearest 100
The digit at tens place is 5, which is equal to 5
So, increase digit 4 at hundreds place by 1
which becomes 24 + 1 = 5
Change 7 at ones place and 5 and tens place to 0
∴ the rounding of 39457 to the nearest 100 is 39500
Rounding to the nearest 1000
Rounding of whole numbers to the nearest 1000 involves checking the digit at hundreds place. If it
is equal to or greater than 5 then the digit at the thousands place is increased by one.
If it is less than 5, then thousands place digit is not increased by one, instead the digits at ones,
tens and hundreds place are set to 0.
if it is equal or greater than 5 then increase the digit at thousands place by one and set the digits at
ones, tens and hundreds place to 0.
Example 1: Round 593795 to the nearest 1000
The digit at hundreds place is 7
7 is greater than 5. So, increase thousands place digit 3 by 1
which becomes 3 + 1 = 4
Change the digits 5 at ones place, 9 at tens place and 7 at hundreds place to 0
∴ the rounding of 593795 to the nearest 1000 is 594000
Example 2: Round off 784129 to the nearest 1000
The digit at hundreds place is 1
1 is less than 5. So, do not increase thousands place digit by 1
Change the digits 9 at ones place, 2 at tens place and 1 at hundreds place to 0
∴ the rounding of 784129 to the nearest 1000 is 784000
General rounding rule of 5
| Whole number compared to 5 | Rule |
|---|---|
| is less than 5 | do not increase the digit on left by 1 |
| is equal to 5 | increase the digit on left by 1 |
| is greater than 5 | increase the digit on left by 1 |
