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Numbers in General Form

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Numbers in General Form:

Let us take the number 68 and write it as 68 = 60 + 8 = 10 × 6 + 8

In general, any two digit number ab made of digits a, and b can be written as
ab = 10 × a + b = 10a + b.

Similarly, ba = 10 × b + a = 10b + a

Let us now take number 495. This is a three digit number. It can also be written as

495 = 400 + 90 + 5 = 100 × 4 + 10 × 9 + 1 × 5

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.

Example

Write the following number in generalised form.
73

73 = 10 × 7 + 3 ......(ab = 10 × a + b = 10a + b)

Example

Write the following number in generalised form.
129

129 = 100 × 1 + 10 × 2 + 9   ......(abc = 100 × a + 10 × b + 1 × c = 100a + 10b + c)

Example

Write the following in the usual form.
100 × 7 + 10 × 1 + 8

100 × 7 + 10 × 1 + 8 = 718   ......(abc = 100 × a + 10 × b + 1 × c = 100a + 10b + c)

Example

Write the following in the usual form:
100 × a + 10 × c + b

100 × a + 10 × c + b = acb  ......(abc = 100 × a + 10 × b + 1 × c = 100a + 10b + c)

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