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1 Number System
Numbers play an important role in mathematics. We have studied about counting numbers in primary classes.
However, we shall review them here and extend our study to have the ideas larger numbers.
We may express numbers in figures as well as in words.
NOTATION Writing a number infigures is called notation.
NUMERATION Writing a number in words is called numeration.
HINDU - ARABIC SYSTEM OF WRITING NUMBERS
n the Hindu-Arabic system, we use ten symbols, namely 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, called digits or figures, to
represent any number.
A group of digits, denoting a number, is called a numeral. We use place-value system to represent a number.
For a given numeral, we start from the extreme right as : Ones, Tens, Hundreds, Thousands, Ten thousands,
Lakhs, Ten lakhs, etc
EXAMPLE 1. Given below are some numbers arranged in a place-value table. Write each number in words and
put it in the expanded form.
PERIOD Lakhs Thousands Ones
→
Ten lakhs lakhs Ten thousands Thousands Hundreds Tens Ones
(i) 9 6 3 8
(ii) 8 2 7 6 5
(iii) 3 5 6 8 0 4
(iv) 5 9 7 3 4 8 2
SOLUTION (i) The given numeral is ‘9638’.
It is ‘nine thousand six hundred thirty-eight’.
In expanded form, we write it as:
9638 = (9 × 1000) + (6 × 100) + (3 × 10) + (8 × 1).
(ii) The given numeral is ‘82765’.
It is ‘eighty-two thousand seven hundred sixty-five’.
In expanded form, we write it as:
82765 = (8 × 10000) + (2 × 1000) + (7 × 100) + (6 × 10) + (5 × 1).
(iii) The given numeral is ‘356804’.
It is ‘three lakhfifty-six thousand eight hundred and four’.
In expanded form, we write it as:
356804 = (3 × 100000) + (5 × 10000) + (6 × 1000) + (8 × 100) + (0 × 10) + (4 × 1).
