Quinary Facts for Kids

Quick facts for kids Numeral systems by culture
Hindu–Arabic numerals
Western Arabic Eastern Arabic Khmer	Indian family Brahmi Thai
East Asian numerals
Chinese Suzhou Counting rods	Japanese Korean
Alphabetic numerals
Abjad Armenian Cyrillic Ge'ez	Hebrew Greek (Ionian) Āryabhaṭa
Other systems
Attic Babylonian Egyptian Etruscan	Mayan Roman Urnfield
List of numeral system topics
Positional systems by base
Decimal (10)
2, 4, 8, 16, 32, 64
1, 3, 9, 12, 20, 24, 30, 36, 60, more…

Quinary (also called base 5 or pental) is a special way of counting. It uses the number five as its main base. Think about your hands! You have five fingers on each hand. This might be why people first started using a base-5 system.

In the quinary system, we only use five different symbols for numbers. These are 0, 1, 2, 3, and 4. When you reach five, you don't have a symbol for it. Instead, you write it as 10. This is similar to how we write ten as 10 in our everyday base-10 system. So, five is 10 in quinary. Twenty-five becomes 100, and sixty is written as 220.

Since five is a prime number (it can only be divided evenly by 1 and itself), some interesting things happen with fractions. Only fractions that have powers of five in their bottom part (like 1/5, 1/25) will have a short, ending decimal in quinary. Other fractions might have repeating patterns.

Understanding Quinary Numbers
See also

Understanding Quinary Numbers

How Quinary Compares to Other Systems

Let's see how the quinary system works by comparing it to other number systems you might know. This includes our common decimal (base 10) system and the binary (base 2) system used by computers.

Quinary Multiplication Table

This table shows how multiplication works in the quinary system. It might look a bit different at first!

A quinary multiplication table
×	1	2	3	4	10	11	12	13	14	20
1	1	2	3	4	10	11	12	13	14	20
2	2	4	11	13	20	22	24	31	33	40
3	3	11	14	22	30	33	41	44	102	110
4	4	13	22	31	40	44	103	112	121	130
10	10	20	30	40	100	110	120	130	140	200
11	11	22	33	44	110	121	132	143	204	220
12	12	24	41	103	120	132	144	211	223	240
13	13	31	44	112	130	143	211	224	242	310
14	14	33	102	121	140	204	223	242	311	330
20	20	40	110	130	200	220	240	310	330	400

Counting in Quinary, Binary, and Decimal

This table shows how numbers from zero to twenty-five look in different number systems. See if you can spot the patterns!

**Numbers zero to twenty-five in standard quinary**
Decimal	0	1	2	3	4	5	6	7	8	9	10	11	12
Quinary	0	1	2	3	4	10	11	12	13	14	20	21	22
Binary	0	1	10	11	100	101	110	111	1000	1001	1010	1011	1100

Quinary	23	24	30	31	32	33	34	40	41	42	43	44	100
Binary	1101	1110	1111	10000	10001	10010	10011	10100	10101	10110	10111	11000	11001
Decimal	13	14	15	16	17	18	19	20	21	22	23	24	25

Quinary in Real-World Languages

Many languages around the world use number systems based on five. This shows how natural counting by fives can be. Some examples include the Gumatj, Nunggubuyu, Kuurn Kopan Noot, Luiseño, and Saraveca languages.

The Gumatj language, spoken in Australia, is a great example. It uses a "5–25" system. This means that 25 is seen as a higher group of 5. Here are some Gumatj numbers:

Number	Base 5	Numeral
1	1	wanggany
2	2	marrma
3	3	lurrkun
4	4	dambumiriw
5	10	wanggany rulu
10	20	marrma rulu
15	30	lurrkun rulu
20	40	dambumiriw rulu
25	100	dambumirri rulu
50	200	marrma dambumirri rulu
75	300	lurrkun dambumirri rulu
100	400	dambumiriw dambumirri rulu
125	1000	dambumirri dambumirri rulu
625	10000	dambumirri dambumirri dambumirri rulu

It's interesting to note that people might not always use exact numbers for very high counts in these languages. Sometimes, the system was explored to higher numbers with a single speaker. This shows how languages can change and grow.

Exploring Biquinary Systems

A biquinary system is a type of decimal (base 10) system. But it uses two smaller bases: two and five. This means it groups numbers by twos and fives.

Roman Numerals: An Ancient Biquinary System

Roman numerals are a famous example of an early biquinary system. You've probably seen them before! The numbers 1, 5, 10, and 50 have their own symbols: I, V, X, and L. For example, seven is written as VII, and seventy is LXX.

Here are the main Roman numeral symbols:

Roman	I	V	X	L	C	D	M
Decimal	1	5	10	50	100	500	1000

Roman numerals are not like our modern number system where the position of a digit matters (like in 123, the '1' means 100). In Roman numerals, the order usually goes from largest to smallest. However, sometimes a smaller number comes before a larger one, like IV (which means 5-1=4) or IX (10-1=9). There is also no symbol for zero in Roman numerals.

Biquinary in Tools and Technology

A Chinese Abacus, also known as a suanpan.

Many types of abacus, like the Chinese suanpan and the Japanese soroban, use a biquinary system. This makes calculations easier. You can see beads grouped in fives and ones.

Other ancient counting methods also used biquinary ideas. These include Urnfield culture numerals and some tally mark systems. Even today, units of currencies often use biquinary groupings. For example, we have 5-cent and 10-cent coins.

Early computers, such as the Colossus and the IBM 650, used a system called Bi-quinary coded decimal. This was a way to represent decimal numbers using biquinary principles.

Quinary on Calculators and in Programming

It's not very common to find calculators that can work with the quinary system. However, some Sharp calculators, like certain models in the EL-500W and EL-500X series, do support it. They often call it the pental system. The open-source scientific calculator WP 34S also includes quinary calculations.

Quinary facts for kids

Contents