The mathematics in class 6th is highly crucial for the students to understand as it will provide them with the right foundation to understand and apply mathematics in further years of their study. The first and foremost chapter that is discussed in the class 6th mathematics NCERT book is called ‘Knowing the numbers’ which discusses the very basis of mathematics i.e. the numbers. It covers the comparison of numbers along with their usage in various situations to give different perspectives on things. You can practice through RS Aggarwal Solutions for Class 6.
Below are some important concepts discussed in the chapter :
- Comparison of numbers
There are many ways you can use to determine the largest and the smallest number in a group but the easiest way is to go by a stepwise method, let us take up a group of numbers, for example – 22, 322, 3567
Here, we just count the number of digits in each number and the number with the highest number of digits is the largest and the one with the lowest number of digits is the smallest. This means 3567 is the highest and 22 is the lowest.
If we have a group with the same number of digits then we have to see the first digit from the left and the number with the highest value of the first digit is the largest and the one with the smallest value of the first digit is the lowest. For example – 3211, 4211, 7233
Here, 7233 is highest with first digit 7, and 3211 is lowest with first digit 3.
If the first or the subsequent digits also fall the same then you must move to the immediate next digit and the number with a lower digit value is smaller and with the higher digit value is larger.
- Arranging numbers in ascending – descending order
Ascending order means keeping the group of numbers in such a way where the lowest comes first and the largest comes last.
Descending order means keeping the group of numbers in such a way that the highest comes first and the lowest comes last.
You can use the concept of comparison of numbers to arrange them in ascending as well as descending orders. For example – 22, 322, 3567, 3211, 4211, 7233
Applying the concept of comparison of numbers we have –
Ascending order – 22, 322, 3211, 3567, 4211, 7233
Descending order – 7233, 4211, 3567, 3211, 322, 22
- Creating largest and smallest number without repeating
When we are given a group of numbers to create the smallest and the largest value without repetition we have to arrange them in ascending order to get the smallest number and then in descending order to get the largest number. For example, we have – 1, 2, 3, 4.
The smallest number is 1234 and the largest number comes out to be 4321. We have got them by arranging the given digits into ascending and descending order respectively.
- Place values of digits
The place value of a number is nothing but an expansion of the given number as an addition of the value of each digit –
For example- 23 = 2(10) + 3(1) ; 431 = 4(100) + 3(10) + 1(1)
- Putting commas in between large numbers
The practice of putting commas in between large numbers is to make the process of reading and writing large numbers easy. There are two main systems that we are going to follow i.e. the Indian and the international system. We follow different methods to put commas in large numbers as per the two systems :
According to the Indian system, we put the first comma after 3 digits from the extreme right of the number and then after every two digits till you reach the extreme left of the number. For example – 1,23,45,678 and it is read as one crore twenty-three lakh forty-five thousand six hundred and seventy-eight.
According to the international system, we have to put the first comma after 3 digits from the extreme right of the number and then after every two digits till you reach the extreme left of the number which is the same as the Indian system but the way to read the numbers in international systems differ significantly. For example – 1,23,45,678 and it is read as one billion twenty-three million forty-five thousand six hundred and seventy-eight.
- Approximations and rounding off
Approximations are done whenever it is difficult to portray the exact value of the number. The main way to approximate a value is done by rounding off the number to the nearest tens, hundreds or thousands.
Whenever we approximate a number by rounding it off then the exact figures are not discussed but a near value is put forth.
For example – The approximation of 23 can be said as 20 or 30 but is closer to the original value it is considered as a more accurate rounded-off approximation.
Some more examples – 36 is rounded off to 40, 521 is rounded off to 500, 3216 is rounded off to 3000.
Rounding off to nearest 10s – Approximates the number to the nearest multiple of 10. Eg- 521 is 520.
Rounding off to nearest 100s – Approximates the number to the nearest multiple of 100. Eg – 521 is 500.
Rounding off to nearest 1000s – Approximates to the nearest multiple of 1000. Eg- 1221 is 1000.
- Approximation of sum of numbers
The Sum of numbers can be approximated by individually rounding off the numbers whose addition needs to be done.
For example – 2331 + 321 = 2652 is added as 2000 + 300 = 2300
- Approximation of product of numbers
The procedure to the approximation of products goes the same as the addition of products with individual rounding off of the participating numbers.
Examples can be given as – 12 X 42 = 504 can be approximated as rounding off the participating numbers and thus giving us a near answer i.e. 10 X 40 = 400.
So, the above summary of class 6th mathematics chapter one can be used to gain an understanding of the chapter.