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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 - Bank PO 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 (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 : 2

In a two-digit number,the digit in the units place is four times the digit in the tens place and sum of the digits is equal to 10. Find the number.
A. 32	B. 14	C. 37	D. 28
Right Option : D
View Explanation