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Introduction
You have studied various types of numbers such as natural numbers, whole numbers,
integers and rational numbers. You have also studied a number of interesting properties
about them. In Class VI, we explored finding factors and multiples and the relationships
among them.
In this chapter, we will explore numbers in more detail. These ideas help in justifying
tests of divisibility.
16.2 Numbers in General Form
Let us take the number 52 and write it as
52 = 50 + 2 = 10 × 5 + 2
Similarly, the number 37 can be written as
37 = 10 × 3 + 7
In general, any two digit number ab made of digits a and b can be written as
ab = 10 × a + b = 10a + b
What about ba? ba = 10 × b + a = 10b + a
Let us now take number 351. This is a three digit number. It can also be written as
351 = 300 + 50 + 1 = 100 × 3 + 10 × 5 + 1 × 1
Similarly 497 = 100 × 4 + 10 × 9 + 1 × 7
In general, a 3-digit number abc made up of digits a, b and c is written as
abc = 100 × a + 10 × b + 1 × c
= 100a + 10b + c
In the same way,
cab = 100c + 10a + b
bca = 100b + 10c + a and so on.
Playing with Numbers
CHAPTER
16
Here ab does not
mean a × b!
250 MATHEMATICS
TRY THESE
1. Write the following numbers in generalised form.
(i) 25 (ii) 73 (iii) 129 (iv) 302
2. Write the following in the usual form.
(i) 10 × 5 + 6 (ii) 100 × 7 + 10 × 1 + 8 (iii) 100 × a + 10 × c + b
16.3 Games with Numbers
(i) Reversing the digits – two digit number
Minakshi asks Sundaram to think of a 2-digit number, and then to do whatever she asks
him to do, to that number. Their conversation is shown in the following figure. Study the
figure carefully before reading on.