Never confuse education with intelligence, you can have a PhD and still be an idiot.
- Richard Feynman -

# Numbers - how to write them

## Background

We get quite a lot of questions from students regarding various prefixes like mega, giga, etc. What do they stand for? What symbol should we use?

It's rather easy to make mistakes with the symbols for the prefixes (and I'm sure you can find tons of such mistakes here on the wiki). But if you really want to know, we'll list a few here (and this time we'll be careful to make it right).

The SI system uses a lot of prefixes for unit quantities, and we'll present a few of them here:

Name Symbol Base 10 As a number Short scale name
peta P  1015 1 000 000 000 000 000  quadrillion
tera T  1012 1 000 000 000 000  trillion
giga G  109 1 000 000 000  billion
mega M  106 1 000 000  million
kilo k 103 1 000  thousand
hecto h 102 100  hundred
deca da 101 10  ten

## What can go wrong if you write numbers the wrong way?

The following amounts (research funding that our appartment applied for) where published on a university website. On the same page. Take a few seconds to think about how much money (Swedish Kronor, SEK) the following stands for:

• `SEK 3 181 million`
• `SEK 1,998 million`
• `SEK 5 994 million`
• `SEK 11,605 million`
• `NOK 1868 million`

Can you find any inconsistencies?

Let's start with the magnitude of the amounts. How likely is it that a researcher has applied for `SEK 11,605 million`? That's `SEK 11,605,000,000` or SEK 11.605 * 109 or more than 11 billion Swedish kronor (Swedish: mer än 11 miljarder kronor).

What are the recommendations for writing large numbers in English? We don't know if there are competing recommendations, but we'll stick with the recommendations from Uppsala University.

Use comma as a separator between thousands: `1,000`, `10,000`, `100,000`, `1000,000` .

Of the quoted amounts on the page we found, there's actually only two amounts that are written correctly (disregarding the fact that the amount is off by a factor of one thousand). That's `SEK 11,605 million` and `SEK 1,998 million`. Eleven thousand six hundred and five million, so the comma comes after 11, and 1 thousand nine hundred and ninety-eight respectively.

`SEK 3 181 million` and `SEK 5 994 million` are wrong, because they use a space as separator of the thousands instead of a comma. Correct would be `SEK 3,181 million` and `SEK 5,994 million`

`NOK 1868 million` is wrong, because it doesn't use any separator at all. Correct would be `NOK 1,868 million`

But it looks a bit confusing to say even `NOK 1,868 million`. We have a name for that number, `NOK 1.868 billion` (US, Eastern Europe, English Canadian, Australian, and modern British) or `NOK 1.868 milliard` (in Western, Central Europe, older British, and French Canadian), but then we must keep in mind that a point is used as a decimal separator while a comma is used as a separator for thousands. Perhaps `NOK 1,868,000,000` is easier? At least now it is clear that the amount is way too high.

For Swedish readers (and, we guess everyone else too), it is a mess that there are two English words for 1,000,000,000 - billion (most commonly used) and milliard (older use). In Swedish, the word is "miljard".

The number 1,000,000,000,000 is called biljon in Swedish, and Trillion using the (most commonly used) short scale in English, and Billion using the long scale English (not so common).

The "next" number, 1,000,000,000,000,000 (1015) is called 'biljard' in Swedish (using the long scale), and most commonly called 'Quadrillion' in English (using the short scale).

The confusion, is, as you see, total. That's why we encourage you to learn the SI standard prefixes from the table above.

If you see Mega (M), you should know that it means 106, or 1,000,000 (a one with six zeros).

If you see Giga (G), you should know that it means 109, or 1,000,000,000 (a one with nine zeros).

If you see Tera (T), you should know that it means 1012, or 1,000,000,000,000 (a one with nine zeros).

If you see Peta (P), you should know that it means 1015, or 1,000,000,000,000,000 (a one with 15 zeros).

And, if you ever write a press release about money, you should know the difference between 3,181 million and 3.181 million. 3,181 is three thousand one hundred and eighty-one. Three thousand millions is three billions (or in Swedish three miljarder), that is 3 x 109. 3.181 million, is three point 181 million, since the English language uses a dot for decimal separator.

If you are unsure, write out all the zeros. The abbreviation for SEK 3 million (3 x 106) in Swedish is 3 mnkr.

But at least, don't mix the formats like mentioned above. In English, use comma between thousands and a dot as the decimal separator. So, 3.0 million is the same as 3 million, or 3,000,000. In Swedish, 3 mnkr is then the same as 3 000 000 kr. Swedish uses a space between thousands.

Especially if you are writing about money, it is important to get this correct. If you were handing out research grants, would you be keen to fund someone who doesn't know the difference between 3,000,000 and 3,000,000,000? Of course, you wouldn't.