The Hindu number system
Ten digits, one per place, and 0 holds the empty places.
Ten symbols for every number
Our own number system gives the numeral 375. It reads as
(3) × 10² + (7) × 10 + (5) × 1
Only the symbols 0 to 9 were used.
How many different symbols do we need to write numbers as big as we like?
What this lesson covers
The idea
The Hindu (Indian) number system is a base-10 place value system using the ten digits 0–9, with a single digit in each position and 0 as a digit, so every number is written unambiguously.
Ten symbols for every number
Our own number system gives the numeral 375. It reads as (3) × 10² + (7) × 10 + (5) × 1 Only the symbols 0 to 9 were used.
How many different symbols do we need to write numbers as big as we like?
- Ten
- One for every landmark number
- No amount is enough
Build with ten digits
Change the digits with ▲ ▼ to build each number. Each place is a power of 10.
A place value system with zero
The Hindu (Indian) number system is a base-10 place value system using the ten digits 0–9, with a single digit in each position and 0 as a digit, so every number is written unambiguously.
375 = (3) × 10² + (7) × 10 + (5) × 1 Indian mathematicians also treated 0 as a number in its own right, on par with other numbers.
Notes
The Hindu (Indian) number system is a base-10 place value system using the ten digits 0–9, with a single digit in each position and 0 as a digit, so every number is written unambiguously.
Check yourself
In the numeral 375, what is the value of the digit 7?
Answer: 70
375 = 3 × 100 + 7 × 10 + 5 × 1, so the 7 stands for 7 × 10 = 70.
Write 6 × 10³ + 0 × 10² + 4 × 10 + 8 as one numeral.
Answer: 6048
Thousands 6, hundreds 0, tens 4, ones 8: the numeral is 6048.
Why can the Hindu number system always be read without confusion?
Which statement about the Hindu number system is true?
- It uses 0 as a digit and a single digit in each position — correct. Yes! Every place has exactly one digit, and 0 holds the empty places.
- It has a separate symbol for each landmark number. That would need endless symbols. This system uses only ten digits and the place of each digit.
- Empty places are left blank. Blanks cause confusion. The Hindu system writes 0 in every empty place.
- It is a base-10 place value system with the digits 0 to 9 — correct. Yes! Its landmark numbers are the powers of 10.
- It is a base-60 system. Base 60 was the Mesopotamian system. The Hindu system is base 10.
- It has no symbol for 0. It has used 0 for more than 2000 years, as a digit and as a number.
- It needs a new symbol for every bigger landmark. It needs no new symbols. The place of each digit tells the landmark number.