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
Fig: 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.
Videos for Quinary Number System
The Real Number System
Questions and Answers
Convert the quinary numbers into decimal numbers.
325
Solution:
325 = 3 × 51 + 2 × 50
325 = 3 × 5 + 2 × 1
325 = 15 + 2
325 = 17
Convert quinary numbers into decimal numbers.
13245
Solution:
13245 = 1 × 53 + 3 × 52 + 2 × 51 + 4 × 50
13245 = 1 × 125 + 3 × 25 + 2 × 5 + 4 × 1
13245 = 125 + 75 + 10 + 4
13245 = 214
Convert decimal numbers into quinary numbers.
134
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 × 52 + 1 × 51 + 4 × 50
134 = 1014
∴ 134 = 10145
Convert 125 into quinary number system into decimal numbers.
Solution:
Here, 125 = 1 × 51 + 2 × 50
= 1 × 5 + 2 × 1
= 5 + 2
= 7 ans.
Convert 425 into quinary numbers into decimal numbers.
Solution:
Here, 425 = 4 × 51 + 2 × 50
= 4 × 5 + 2 × 1
= 20 + 2
= 22 ans.
Convert 1205 into decimal number system.
Solution:
Here, 1205 = 1 × 52 + 2 × 51 + 0 × 50
= 1 × 25 + 2 × 5 + 0
= 25 + 10
= 35 ans.
Convert 30425 into decimal number system.
Solution:
Here, 30425 = 3 × 53 + 0 × 52 + 4 × 51 + 2 × 50
= 3 × 125 + 0 + 4 × 5 + 2 × 1
= 375 + 0 + 20 + 2
= 397 ans.
What is quinary number system? Mention its examples too.
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.
Quiz
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