Notes on Quinary Number System | Grade 7 > Compulsory Maths > Operation on Whole Numbers | KULLABS.COM

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#### 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

• 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.
.

### Very Short Questions

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

0%

10012
11002
11012
10102

2
5
3
4
• ### The quinary number system is also known as _______.

the base of five system
the base of six system
the base of two sytem
the best of seven system

335
224
446
113

155
145
135
125

3
9
7
5

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