## Quinary Number System

Subject: Compulsory Maths

#### Overview

Quinary number system consists of five digits 0 to 4 and its base is 5. The number is expressed in the power of 5 in order to convert a quinary into decimal number.

#### Quinary Number System

Quinary number system consists of five digits 0 to 4 and its base is 5. It is also known as the base five system. The number of quinary number system can be expressed in the power of 5.

#### Conversion of quinary number into decimal number

The number is expressed in the power of 5 in order to convert a quinary into decimal number. Then, by simplifying the expanded form of the quinary number, we get a decimal number. For example:
16 = 1× 51 + 6× 50
= 1× 5 + 6× 1
= 5 + 6
= 11

#### Conversion of decimal number into quinary number

We can convert a decimal number into quinary number by using the place value table of the quinary system. For example:
Convert 15 into quinary system

 54 53 52 51 50 625 125 25 5 1 1× 53 1× 52 0 × 51 3× 50 1 1 0 3

Here,
153 = 1× 125 + 1× 25 + 0× 5 + 3× 1
= 1× 53 + 1× 52 + 0× 51 + 3× 50
∴ = 11035

Alternative method
We should dividethe given number successively by 5 until the quotient is zero in order to convert decimal number int quinary number. The remainders of each successive division are then arranged in reverse order to get required quinary number. For example:

 Divisor Dividend Remainders 5 134 4 5 26 1 5 5 0 5 1 1 5 0

Now, arranging the remainders in reverse order: 10145

$\therefore$ 135 = 10145

##### Things to remember
• Quinary system is also known as the base five system.
• The number of quinary number system can be expressed in the power of 5.
• By simplifying the expanded form of the quinary number, we get a decimal number.
• It includes every relationship which established among the people.
• There can be more than one community in a society. Community smaller than society.
• It is a network of social relationships which cannot see or touched.
• common interests and common objectives are not necessary for society.
##### The Real Number System

Solution:

325 = 3 × 51 + 2 × 50
32= 3 × 5 + 2 × 1
32= 15 + 2
32= 17

Solution:

1324= 1 × 53 + 3 × 52 + 2 × 51 + 4 × 50
1324= 1 × 125 + 3 × 25 + 2 × 5 + 4 × 1
1324= 125 + 75 + 10 + 4
1324= 214

Solution:

 54 53 52 51 50 625 125 25 5 1 1 × 53 0 × 52 0 × 51 0 × 50 1 0 1 4

Here,
134 = 1 × 125 + 0 × 25 + 1 × 5 + 4 × 1
134 = 1 × 53 + 0 × 5+ 1 × 51 + 4 × 50
134 = 1014
∴ 134 = 10145

Solution:

Here, 125 = 1 × 51 + 2 × 50

= 1  × 5 + 2 × 1

= 5 + 2

= 7 ans.

Solution:

Here, 425 = 4 × 51 + 2 × 50

= 4 × 5 + 2 × 1

= 20 + 2

= 22 ans.

Solution:

Here, 120= 1 × 52 + 2 × 51 + 0 × 50

= 1 × 25 + 2 × 5 + 0

= 25 + 10

= 35 ans.

Solution:

Here, 30425 = 3 × 53 + 0 × 52 + 4 × 51 + 2 × 50

= 3 × 125 + 0 + 4 × 5 + 2 × 1

= 375 + 0 + 20 + 2

= 397 ans.

The system which has the base of five in which we use only five digits from 0, 1, 2, 3 and 4 is called the quinary number system. The examples of quinary number system are 1025, 23405, 345 etc.