At the very beginning of human civilization, human beings felt the necessity of counting to meet up their daily needs. At the very first stage they used to maintain the records of animals and objects by using various types of symbols, things or sticks of equal size and by drawing lines on floor or stones. But with the development of civilization, the need of other types of symbol was felt for counting the increased number of animals and goods. The system of counting has developed since then and this the present system of using the number has evolved.
At the end of the chapter, the students will be able to
1. enumerate the natural numbers.
2. read by enumerating in national and international system.
3. determine Prime, Composite and Co-prime numbers.
4. explain divisibility.
5. verify the divisibility by 2, 3, 4, 5, 9.
6. find H.C.F. and L.C.M. of common fractions and decimal fractions.
7. solve Mathematical problems by simplifying the common fractions and decimal fractions.
1.1 Enumeration :
In arithmetic, all numbers can be expressed by ten symbols. These symbols are 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. These are also known as digits. Again, these are numbers as well. The numbers except zero are Natural Numbers. Among them, first nine digits are significant digits and the last one is zero. The intrinsic values of the numbers are one, two, three, four, five, six, seven, eight, nine and zero respectively.
All the numbers greater than 9 are written by placing two or more than two digits side by side Any number written in digits is known as the numeration. All these ten symbols are used in enumeration.
The numbers are ten based and that is why, they are called the decimal system or the system of multiples of ten. In this system, the digit on the extreme right side expresses its intrinsic value. The second digit from the right expresses ten times of its intrinsic value.
It is to be noted that the value of any digit used in a number depends on its place in the number. The digit, used in a number, expressing the number due to its place is called the place value of that number.
For example, in the number 333, the place value of the digit 3 on the extreme right is 3; the place value of 3 in the second and the third places from the right are 30 and 300 respectively. Hence, the place value of the same digit differs from place to place, but its intrinsic value remains the same.
i.e. 333 = 3×100+3×10+3
1.2 International counting system
In this system, the places from ones to billions are arranged successively as follows :
The digits in the places of Ones, Tens and Hundreds are read and expressed in words as our local system. The place just to the left of the hundreds is the place of thousands. A number consisting of not more than three digits can be written in the places of thousands and the written number is read as so many thousand. Such as, the written number in thousands in the above table is one hundred eleven and the number is read as one hundred eleven thousand. The place to the left of the thousands 1s the place of millions and a number consisting of not more than three digits can be written in the place of millions.
The written number is read as so many million. Such as, the written number in the place of million in the table is one hundred eleven and itis to be read as one hundred eleven million. The place to the left of million is billion. The number written is read as so many billion. Such as, the number written in the table is one hundred eleven and read as one hundred eleven billion.
A comma (,) is placed after every three digits starting from the right to facilitate the reading of the numbers, which is the international system of counting.
