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Culture and history · How ideas travel

The journey of zero and decimals

Writing 0.125 feels completely natural, yet it is the product of a long journey: ideas that grew up separately in Babylon and India (any transfer between them is undocumented and disputed) travelled from Baghdad to Damascus and Samarkand to Europe. Put in order who added what.

  • 17 min
  • 2 simulations
  • Mini quiz

Updated:

Preview

The question

The receipt for the tomatoes you bought at the greengrocer's says "2.75 kg". Packed into that short figure are three big ideas: a digit whose value depends on where it stands, a zero that marks an empty place, and the decimal fraction, which writes parts smaller than 1 using the same scheme. How would a Roman merchant have written this weight? And who came up with these three ideas? The short answer: nobody did it alone.

Try it yourself

No account needed: change the values and check your answer. Some simulations ask for a prediction before they start; it doesn't matter whether it's right or wrong.

Number line

From base 60 to base 10

Drag the marker, or move it in steps of 0.025 with the arrow keys, then press Check.

Prediction

Predict first

Which of these do you think the base-60 value 0;7,30 is equal to?

It doesn’t matter whether you’re right; the simulation opens once you choose.

Ordering

From place value to decimals: a timeline

Put the cards in order by dragging them or moving them with the keyboard, then press Check.

Prediction

Predict first

Where and when do you think decimal fractions were first used, as far as we know?

It doesn’t matter whether you’re right; the simulation opens once you choose.

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Frequently asked

5 questions

Who invented zero?

No single person. The Babylonians used a placeholder sign for an empty place, and the Maya independently developed a zero sign. It was Brahmagupta in India, in 628, who treated zero as a number you calculate with and wrote down its rules.

Why are our numerals sometimes called "Arabic numerals"?

These numerals and the base-ten system developed in India. Europe learned them mainly through Latin translations of the book al-Khwarizmi wrote in Baghdad and through Fibonacci's Liber Abaci of 1202. That is why historians of science call them "Hindu-Arabic numerals".

Did Europeans invent decimal fractions?

No. The oldest known example is in a book al-Uqlidisi wrote in Damascus in 952–953. Al-Kashi made decimal fractions into a system in Samarkand in 1427. In 1585 Simon Stevin argued for using them in everyday calculation, which helped them spread.

Is a number with more digits after the decimal point bigger?

No. First look at the tenths place: in 0.125 and 0.5 those digits are 1 and 5, so 0.5 is bigger. What makes a number bigger is place value, not the number of digits.

Why does an hour have 60 minutes and a minute 60 seconds?

It is a legacy of the Babylonian number system, whose base is 60. The Babylonians wrote fractions the same way, and astronomers used sexagesimal fractions for centuries. Measuring angles in degrees, minutes and seconds is part of the same legacy.