What is an estimate?
An estimate is a number that is close to the exact number.
You can estimate the sum and the differences by rounding off.
What do you mean by rounding off a number?
Rounding means replacing a number with an approximate number that is simpler than the previous one.
To round a number to a particular place, we need to check the digit to the immediate right of that place. If the digit is 5 or greater than 5, the digit at the required place is incremented by 1. If not, the digit remains the same and all the digits to the right of that digit are replaced with zeroes.
For example:
- If 12346 is rounded to the nearest tens, the number will be 12350.
- If 12346 is rounded to the nearest hundreds, the number will be 12300.
- If 12346 is rounded to the nearest thousands, the number will be 12000.
- If 12346 is rounded to the nearest ten-thousands, the number will be 10000.
How can we estimate sum and difference the using rounding?
The following are the steps you should follow while rounding:
- Round each number to the required place (to the nearest tens, hundreds, and so on).
- Add or subtract the rounded numbers.
For example:
Estimate 2314 + 1231. Round to the nearest tens when estimating.
Upon rounding off the numbers 2314 & 1231 to the nearest tens, we get
2314\(\rightarrow \)2310
1231\(\rightarrow \)1230
Hence, the estimated sum is 3540.
For example:
Estimate 4237 – 1532 Round to the nearest hundreds when estimating.
Upon rounding off the numbers 4237 & 1532 to the nearest hundreds, we get
4237\(\rightarrow \)4200
1532\(\rightarrow \)1500
Hence, the estimated difference is 2700.
Solved Examples
Example 1:
Estimate 23162 – 12524. Round to nearest tens, thousands, and ten thousands to estimate in three ways.
Solution:
Upon rounding off the given numbers to nearest tens, we get
23162\(\rightarrow \)23160
12524\(\rightarrow \)12520
Similarly,
Upon rounding off the given numbers to nearest thousands, we get
23162\(\rightarrow \)23000
12524\(\rightarrow \)13000
Similarly,
Upon rounding off the given numbers to the nearest ten-thousands, we get
23162\(\rightarrow \)20000
12524\(\rightarrow \)10000
Example 2:
Estimate the sum,
17281 + 12754. Round to nearest hundreds and ten-thousands to estimate.
Solution:
Upon rounding of the given numbers according to the place values, we get
17281\(\rightarrow \)17300 (Nearest hundredths)
12754\(\rightarrow \)12800 (Nearest hundredths)
Similarly,
17281\(\rightarrow \)20000
12754\(\rightarrow \)10000
Example 3:
Daisy has walked 210 yards more than Noah. If Noah has walked a total of 1520 yards, approximately how much has Daisy walked in total?
Solution:
We need to find an approximate value. Hence, we can estimate. Let us estimate to the nearest hundreds.
Noah has walked for 1520 yard
Daisy has walked for (1520 + 210) yard
Upon rounding off the distances to the nearest ten, we get
1520\(\rightarrow \)1500
210\(\rightarrow \)200
(1500 + 200) = 1700
Hence, Daisy has walked approximately 1700 yards.
It affects the accuracy of the estimate, as the value of the place to which the digit is rounded to increases, the accuracy of the estimate decreases.
For ease and speed of calculations, numbers can be rounded in a manner that the sum or difference can be easily estimated.