SEBA Class 9 Advanced Mathematics PDF Text Books free Chapter 1
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Here we will discuss the Advanced Maths Class 9 Chapter 1 System of Numeration. Here we will discuss the basic concept of this chapter which will be very useful for the students before starting the Exercise of this chapter. So, if you have any clarity and doubts then please share your problems.
What are Numbers?
The numbers are the concepts that arise in our minds when we
speak questions “how many”, “how much” etc. in any group of things. Numbers we
can not see, but we denote them by different names and symbols.
System of Numeration is a process of writing and reading
numbers expressed in figures.
The base of a Number:
After being able to represent the numbers by one, two, three, etc. there arose a problem. Numbers have no end. So it is not possible to
assign different names or symbols to every different number.
You also know that the symbols which are used for writing
numbers are called the digits.
For example, the ten symbols we mentioned above and which we
are using today base ten are:
0,1,2,3,4,5,6,7,8,
and 9
They are called digits. Likewise,
the Roman symbols, I, V, X…….. etc and the old Greek letters: ∝,Ī², ⋎.... etc. are all digits.
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Any number written with such digits is called a numeral.
4948 = 4 ļ½ 103 + 9 ļ½ 102 + 4 ļ½10 + 8 ļ½1 is called the numeration system in base 10.
Again note that the digits in the number 4948 have different
values according to their places. This value is called the place-value or weight of
that digit.
In a numeral, the number which determines the value of each
digit placed in different places is called the base of the system.
The Roman System:
Like Greeks, Babylonians, the Roman numeration system is also literal. On different occasions, this system is used even today. You have come across these denoting the chapters or part of a book or in numbering the dials of a clock.
There are seven symbols in the Roman system: I, V, X, L, C, D, and M.
How the Romans denoted numbers with the help of these seven
symbols or digits can be understood by looking at the following:
Roman Numeral
| Roman Symbols | Decimal Value |
|---|---|
| I | 1 |
| V | 5 |
| X | 10 |
| L | 50 |
| C | 100 |
| D | 500 |
| M | 1000 |
The fundamental principles of writing numerals by the Roman system are:
š1. A smaller digit is to be added when it is placed just right of a larger digit and is to be subtracted when it is placed on the left of the larger digit.
š2.If a smaller digit is placed between two larger digits, then the smaller digit is always to be subtracted from the right-sided larger digit.
š3. V, L, and D are never to be repeated.
š4. The digits V, L, D, and M are not to be subtracted from any digit.
š5.The value of a digit is increased 1000 times if a bar is placed over the digit.
š6. The left digit of each pair below can be subtracted only once from the right digit.
(I,V), (I,X), (X,L),(X,C),(C,D),(C,M)
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