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Really good Anchor Chart Video for beginners

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Really good Anchor Chart Video for beginners

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This is a video to accompany the "Math Tools in Action: Anchor Charts" article below.

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This is a video to accompany the "Math Tools in Action: Anchor Charts" article below.

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Explicit Vocabluary Instruction Sample Slides

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Tell me how you write large numbers and I'll tell you where you're from.

Well...not really, but there's no doubt numbers with multiple digits and decimals are written in different ways across the globe. For example, number formatting in Europe is not the same as in the US.

If you've ever received an invoice from a contractor in Europe, you might have noticed that some numbers are not written the same way as in America. Instead of a dot between euros and cents you might have seen a comma, and instead of a comma as a thousands separator you might have seen a space or a dot.

Why is the European number format different than the American? It's a long story, but here's the short(er) version.

The decimal separator in Europe

In most European countries, a comma is used to separate the integral part of a number from the decimal part. This means, for example, that three hundred euros and ten cents is written as 300,10-with a comma as a decimal marker.

On the other hand, in the US-as well as in other English-speaking countries including Australia, New Zealand, and the UK-the same amount is written as 300.10, using a decimal point.

In general, some countries use a period before decimals, while many other countries use a comma. And still other countries, such as Canada, use both: British Canada uses a point, while French Canada uses a comma.

Why do European countries use a comma instead of a decimal point?

Throughout history, mathematicians have used all kinds of symbols to separate integers from decimals, including the dot, comma, inverted comma, vertical bar, horizontal line, colon, semicolon, and even number zero. Especially in the 17th and 18th centuries, it seems that mathematicians used whichever notation seemed to strike their fancy, and so did typesetters. How people learned math back then is a mystery to me.

Which came first, the decimal point or the decimal comma?

The decimal point, it seems, though historians of mathematics aren't certain. In the 16th century, Italian cartographer Giovanni Antonio Magini and German mathematician Christopher Clavius were among the first to use a decimal point in their publications. But the person who popularized the use of the decimal point was the inventor of logarithms (one of my high school nightmares), Scottish mathematician John Napier. Thanks to the English translation of Napier's treatise on logarithms, the decimal point became widespread in Britain as far back as the 17th century.

What happened in continental Europe? For a while, the decimal point was used, though some preferred the decimal comma. Things changed in the 18th century, when another famous mathematician, Gottfried Wilhelm Leibniz-the father of integral and differential calculus (another of my high school nightmares)-introduced the dot as a symbol for multiplication: "I do not like × as a symbol for multiplication, as it is easily confounded with x", he wrote. He was an influential mathematician, and the dot as a multiplication sign became widespread in Europe. But this solution created another problem: The dot as a multiplication sign could be confused with the decimal point, so European mathematicians started to use a comma to separate decimals. The comma as a decimal separator became standard in Europe in early 19th century, and still remains so today.

American mathematicians didn't follow the lead of their European counterparts. In the 18th century, the cross (×) was more popular as a multiplication sign than the dot in America, so the dot continued to be used to separate decimals from whole figures. Even when in the 19th century the dot became the standard symbol for multiplication in the United States, the decimal separator didn't change. Till today, it remains the dot on the baseline (.), while the multiplication symbol is a raised dot (·).

Though the decimal point was invented in Europe, it's Leibniz's "fault" that today in continental Europe we use a decimal comma, while in most English-speaking countries a decimal point is used.

The International System of Units: Symbol for decimals

If you're writing a scientific or technical document, you'll need to follow the International System of Units. In the SI System, the decimal marker is either the comma or the dot (to be more precise, the point on the line). "The decimal marker chosen should be that which is customary in the context concerned."

Writing numbers with decimals-SI System:
100,33 and 100.33 (In the US, a dot is recommended.)

The thousands separator in Europe

When it comes to formatting numbers, the differences between the European and American systems don't end with the decimal marker. There's one more important difference: When writing large numbers (tens of thousands or more), in Europe we use either a dot or a thin space to separate groups of three digits-counting from both the left and the right of the decimal separator.

For example, in Europe we write three hundred thousand either as 300.000 (groups of three digits separated by a dot) or 300 000 (groups of three digits separated by a thin space). Whether a dot or a space is used differs by country, but in Europe we never use a comma for this purpose. That would be confusing, because the comma is our decimal separator.

In the US, however, groups of three digits in large numbers are marked off with a comma (300,000 means three hundred thousand).

So, if your web designer in Spain sends you an invoice for 10.000,45 euros, or your project manager in Denmark sends you an invoice for 10 000,45, it means ten thousand euros and forty-five cents. A vendor in the US would write the same amount as 10,000.45.

The International System of Units: Writing large numbers

According to the International System of Units, to facilitate reading, numbers with many digits (usually, at least five before or after the decimal marker) can be divided in groups of three digits by inserting a thin space. No periods or commas should be used to group digits. So, while in American English it's correct to use commas to separate groups of three digits, if you need to follow the SI, do not use commas; use thin spaces or no punctuation at all.

Writing large numbers in SI System:
101 000,330 245 and 101 000.330 245
101000,330245 and 101000,330245
Not: 101,000.330,245 and 101.000,330.245

Update 26 April 2020: Thanks to M. Payne for sending me the link to Resolution 10 of the 22nd General Conference on Weights and Measures (2003), which

"reaffirms that 'Numbers may be divided in groups of three in order to facilitate reading; neither dots nor commas are ever inserted in the spaces between groups', as stated in Resolution 7 of the 9th CGPM, 1948".

Maybe the authors of style guides should take a firmer stance and emphasize the importance of such recommendations for all kinds of writing, and not just scientific writing.

European number format examples

If you're wondering how we format currency in Europe, or how we format large numbers or numbers with decimals, here are some examples:

Most European countries (as well many other countries in the world):
300.000 or 300 000 means three hundred thousand
€120.000,99 or €120 000,99 means one hundred twenty thousand euros and ninety-nine cents

The UK (plus other countries in the world, like the US, Australia, and New Zealand):
300,000 means three hundred thousand
€120,000.99 means one hundred twenty thousand euros and ninety-nine cents

SI System:
300 000 means three hundred thousand
€120 000,99 or €120 000.99 means one hundred twenty thousand euros and ninety-nine cents

Summary: Number formatting in Europe

Most European countries use a comma as a decimal marker, and separate groups of three digits in large numbers with a dot or a thin space (non-breaking space in electronic publications). Americans-as well as the British and the Irish-use a decimal point, and they mark off groups of three digits in large numbers with commas. The SI System accepts both the decimal point and the decimal comma, but it doesn't accept the comma as a thousands separator.

If authors from different parts of the world contribute to your document, pay extreme attention to the way numbers are formatted. Thorough editing and proofreading will ensure the consistency and accuracy of the numbers in your text-which is crucial, because a mistake in number formatting may be costly.

Do you have a document that needs editing or proofreading? Send me a message at editor@languageediting.com
Similar post: A coffee costs €2: The plural of euro

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Tell me how you write large numbers and I'll tell you where you're from. Well...not really, but there's no doubt numbers with multiple digits and decimals are written in different ways across the globe. For example, number formatting in Europe is not the same as in the US.

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6-12 Tiered Language Acquisition Graphic

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6-12 Tiered Language Acquisition Graphic

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Your grade depends on it!

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Participant Guide for Math Vocabulary Development for ALL Students

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Participant Guide for Math Vocabulary Development for ALL Students

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ITC Copy of PM Copy of K-12 pm Developing Math Vocabulary Participant Guide - Google Docs.pdf

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1) Open & Copy 2) Share with martine.harrington@lcps.org 3) Add your name and PID to Title Slide.  This document acts as the sign-in and survey.