Numbers in General Form


 
 
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 (b) in the general form 100times a+10times b+c represents for the number 689

Right Option : C
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Explanation
Question : 2

What does the literal (c) in the general form 100times a+10times b+c represents for the number 392

Right Option : D
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Explanation
Question : 3

Find the product of the values of the literal (a) in 325, (b) in 526 and (c) in 987 when the general form is 100times a+10times b+c.

Right Option : D
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Explanation
 
 
 


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