Arithmetic Chapter 3 Logical Approximation Of Number
Arithmetic Chapter 3 To express any number to the nearest multiple of 10, 100, 1000,…. etc. in integers :
1. In our daily life, we often face different types of problems such as “How many populations are there in our village ?” or “How many populations are there in India ?” etc.
2. In answering this type of question, we all generally do not answer the exact correct number of the population. But we say a convenient and approximate nearest integer.
3. For example, in the case of the first question, if the population of the village is 2145, then we say in its answer 2000.
Understanding Approximation in Maths for Kids
4. Again, in the case of the second question, if the correct population in India is one hundred twenty-five crore seventy-five lac twenty-seven thousand seven hundred twenty-two, then we say in answer that the population in India is about one hundred twenty-six crore.
5. The tendency to say this type of answer in integers is remaining with almost all of us.
6. Now the question arises that whether there are any rules to answer in integers or not.
7. We shall illuminate this in the following discussions.
WBBSE Class 6 Logical Approximation Notes
Arithmetic Chapter 3 The Rules To Express Any Number To The Nearest Multiple Of 10, 100, 1000 …… Etc
1. To express a number to the nearest multiple of 10:
- To express a number to the nearest multiple of 10, if the digit in the units place is 5 or greater than 5, then the digit in the tens place increases by 1, and the digit in the units place will be 0.
- To express a number of nearest multiple of 10, if the digit in the units place is less than 5, then the digit in the tens place will be the same and the digit in the units place will be 0
2. To express a number to the nearest multiple of 100.
- To express a number to the nearest multiple of 100, if the digit in the tens place of the number is less than 5, then the hundreds place digit of the number will be the same as before, and the digits in the tens place and the units place both will be zero.
- To express a number to the nearest multiple of 100, if the digit in the tens place of the number is 5 or greater than 5 then the digit in the hundreds place increases by 1 and both the digits.
- In the tens place and the units, the place should be 0.
Important Definitions Related to Approximation
3. To express a number to the nearest multiple of 1000.
- To express a number to the nearest multiple of 1000, if the digit in the hundred places of the number is less than 5, then the thousand place digit will be the same as before and the digits in the hundreds place, tens place, and the units place all will be 0.
- To express a number to the nearest multiple of 1000, if the digit in the hundred places of the number is 5 or greater than 5, then the digit in the thousands place increases by 1, and all the digits in the hundreds, tens, and units place is 0.
4. General rule To express a number to the nearest multiple of 10n (n = 1, 2, 3, ), if the digit in nth place (from right) is
- less than 5, then (n + 1)th digit will be the same as before and all the next digits will be zero.
- 5 or greater than 5 then (n + 1)th digit increases by 1 and next all digits should be zero.
Examples of Real-Life Applications of Approximation
Example: Suppose that we want to express a number to the nearest multiple of 107 = 10000000 in an integer. Then if the 7th place digit (from right) i.e., the digit in the ten lacs place is
- less than 5, then the digit in the 8th place i.e., the digit in the crores place will be the same as before and all the next digits i.e., ten lac, lac, ten thousand, thousand, hundred, tens, units places will be 0.
- 5 or greater than 5, then the digit in the 8th place i.e., the digit in the crores place increases by 1, and all the next place digits should be zero.
You observe the following examples so that you will have a clear concept about the above discussions and also about the chapter.