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Numbers & Arithmetic: fun facts and quiz
The essentials in 7 ideas, with fun facts, an illustrated story and a quiz to see how much you know.
The essentials
The Story of Zero
Zero as a number in its own right, not just a gap, was developed in India. Brahmagupta wrote rules for calculating with it in 628 CE.
Key fact
You can’t divide a number by zero.
Place Value
In our number system, a digit’s position sets its value: in 352, the 3 means three hundreds. That’s how ten digits can write any number.
Key fact
Our digits are called Hindu-Arabic numerals.
Prime Numbers
A prime number can only be divided evenly by 1 and itself, like 2, 3, 5, 7 and 11. There are infinitely many, as Euclid proved over 2,000 years ago.
Key fact
2 is the only even prime number.
Negative Numbers
Negative numbers go below zero, like −5 °C or an overdrawn bank account. Chinese mathematicians used them around 2,000 years ago, with red and black counting rods.
Key fact
A negative times a negative makes a positive.
Fractions & Decimals
Fractions and decimals are two ways to write parts of a whole: ½ = 0.5 and ¼ = 0.25. A percentage is just a fraction out of 100.
Key fact
⅓ as a decimal goes on forever: 0.333…
Really Big Numbers
A million is a thousand thousands; a billion is a thousand millions. A googol, 1 followed by 100 zeros, gave Google its name.
Key fact
A million seconds is about 11.5 days; a billion is about 31.7 years.
Pi
Pi is a circle’s circumference divided by its diameter: about 3.14159. Its digits go on forever without repeating.
Key fact
Pi Day is celebrated on 14 March: 3/14.
Fun facts
The Maya invented their own zero independently, often drawn as a shell, centuries before zero reached Europe.
Europe didn’t trust the new digits at first: in 1299, Florence banned them from bank records because they were easier to forge.
Some cicadas come out every 13 or 17 years. Both are primes, which may help them avoid predators that follow shorter cycles.
For centuries many European mathematicians rejected negative numbers. In 1544 one still called them “absurd numbers”.
Ancient Egyptians wrote fractions as sums of unit fractions: ¾ was ½ + ¼.
The word “googol” was coined in 1920 by a nine-year-old boy, the nephew of mathematician Edward Kasner.
In 1897, a bill in Indiana nearly fixed a wrong value of pi into law; the state senate shelved it.
Story: The Merchant’s Son and the Digits
The Merchant’s Son and the Digits
Around 1200, young Leonardo of Pisa travels with his merchant father to North Africa, and learns a new way of writing numbers.
Ten digits, zero included, make sums far easier than Roman numerals. In 1202, he explains them to Europe in a book, Liber Abaci.
Merchants slowly switch over. We know him by his nickname, Fibonacci, thanks to a puzzle about breeding rabbits in that same book.
True or false?
Tap your answer to see if you got it, and why.
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Question 1 of 10
Brahmagupta treated zero as a number in its own right.
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True. With rules for adding and subtracting it.
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Question 2 of 10
In 352, the 3 stands for three hundred.
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True. Its position gives it the value.
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Question 3 of 10
2 is a prime number.
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True. And the only even prime.
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Question 4 of 10
A negative number times a negative number is positive.
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True. −2 × −3 = 6.
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Question 5 of 10
½ is the same as 0.5.
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True. And 50%.
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Question 6 of 10
Google’s name comes from the number googol.
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True. A playful misspelling.
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Question 7 of 10
Pi’s digits go on forever without repeating.
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True. It’s an irrational number.
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Question 8 of 10
Dividing a number by zero gives zero.
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False. Division by zero isn’t defined.
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Question 9 of 10
Roman numerals use place value just like ours.
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False. Roman numerals add and subtract symbols instead.
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Question 10 of 10
1 is a prime number.
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False. By definition, primes must be greater than 1.
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KnowSoda learns what you know and brings back what you’re about to forget. Numbers & Arithmetic has 6 more ideas at the Advanced and Expert levels.
Sources
- MacTutor History of Mathematics — Brahmagupta, zero, Chinese negative numbers
- Khan Academy — Arithmetic and pre-algebra
- Euclid, Elements, Book IX, Proposition 20 (infinitely many primes)
- Encyclopaedia Britannica — googol, pi, numerals
- Great Internet Mersenne Prime Search — M136279841 (2024)
