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Numbers in General Form

Number Theory - Concepts

Even and Odd Numbers

Prime and Composite Numbers

Co-Prime and Twin Prime Numbers

Numbers in General Form

Interchanging Digits

Class - EXIM AO Prelims Subjects

Concept Explanation

Numbers in General Form

The numbers can be expressed in the following forms

Expanded form:

Any natural number can be written in the expanded form by using the place values of its digits. For example:

1. $57=10times 5+7$

2. $975=100times 9+10times 7+5$

$5498=1000times 5+4times 100+9times 100+8$

Exponential form:

Any natural number can be expressed in exponential form by using powers of 10 and the digits of the number . For example,

1. $57=10^{1}times 5+10^{0}times 7$

2. $975=10^{2}times 9+10^{1}times 7+10^{0}times 5$

3. $5498=10^{3}times 5+10^{2}times 4+10^{1}times 9+10^{0}times 8$

General Form For a Two-digit Number:

The general form of writing any number is using the literals instead of numbers.Let us now consider a two digit number using literals a and b respectively as tens and units digits.

Using the above notations the number can be written both in expanded form or exponential form as follows:

$10times a+b;;;;or;;;;10^{1}times a+10^{0}times b$

Let us use the notation $overline{ab}$ to denote this number.

i.e, $overline{ab}=10times a+b$ or , $overline{ab}=10^{1}times a+10^{0}times b$

Here, we have put a line over ab to distinguish it from the expression ab, which means a multiplied by b.

This is known as the generalised form of a two digit number.

General Form For a Three-digit Number:

The general form of writing any number is using the literals instead of numbers.Let us now consider a three digit number using literals a, b and c respectively as hundreds, tens and units digits.

Using the above notations the number can be written both in expanded form or exponential form as follows:

$100times a+10times b+c;;;;or;;;;10^{2}times a+10^{1}times b+10^0times c$

Let us use the notation $overline{abc}$ to denote this number.

i.e, $overline{abc}=100times a+10times b+c$ or , $overline{ab}=10^{2}times a+10^{1}times b+10^0times c$

Here, we have put a line over abc to distinguish it from the expression abc, which means a multiplied by b and then multiplied by c.

This is known as the generalised form of a three digit number.

Illustration: What does the literal a in the general form $100times a+10times b+c$ represents for the number 365

Solution: While expressing 365 in expanded form we get

$overline{365}=100times 3+10times 6+5$

on comparing with the general form

$overline{abc}=100times a+10times b+c$

we get a = 3.

Thus the literal a represents 3 in the general form

Sample Questions

(More Questions for each concept available in Login)

Question : 1

What does the literal (c) in the general form $100times a+10times b+c$ represents for the number 392
A. 3	B. 90	C. 9	D. 2
Right Option : D
View Explanation

Question : 2

What does the literal (a) in the general form $100times a+10times b+c$ represents for the number 904
A. 9	B. 900	C. 0	D. 4
Right Option : A
View Explanation

Question : 3

Find the sum of the values of the literal (b) in the general form $100times a+10times b+c$ represents for the number 904, 326, 984
A. 10	B. 9	C. 8	D. 7
Right Option : A
View Explanation