Very large and very small numbers

Dealing with very large or very small can easily be confusing and it can be hard to appreciate e.g. how much larger an (american) billion is than a million. One way is to think in time: One million seconds (1e6 s) equals about 11.6 days, whereas one billion seconds (1e9 s) equals just over 31 years.

Note that I specify an “American billion”, as in English, “billion” and “trillion” can mean very different numbers, depending on whether you are using the “Short scale” (common in USA and more and more common in the UK) or the “Long scale” (used in many languages, such as French and Swedish). A billion in the Long scale is 1000 times larger than a billion in the Short scale. A Long scale trillion (1e12) is a million (1e6) times larger than a Short scale trillion (1e18). See the figure below for the difference between the Short and Long Scales.

The Corona relief package, passed recently in the US congress, was about 2 trillion USD. Written out that would be 2 000 000 000 000 USD. Nobody likes to count zeros, so an easier way to write the value is 2e12 USD, as we do in Physics. An even easier way is to use the SI prefixes (See the figure below), where “k” equals 1e3, “M” equals 1e6″, “G” equals 1e9 and “T” equals 1e12. This way,2 trillion USD can easily be written as 2 TUSD. This is 1000 times larger than 1 GUSD. A million euros would be 1 MEUR. Note that these prefixes are case sensitive: 1 mEUR equals 0.001 EUR! You will notice that these prefixes are the same as are used in scientific units like kg, km, or MPa; or in computer science units like Mb/s (mega-bit per second), GB, or PB (peta-bytes).

Now that we know the prefixes, it is easier to talk about large numbers and perhaps remember them. E.g. the largest company on the Finnish stock exchange is Neste with a market value of 42 GEUR (“giga-euro”). On the US market, Apple is the largest with a value of 1.85 TEUR (“tera-euro”). For comparison, the state budget of Finland 2020 was ~58 GEUR.

The Gross Domestic Product (GDP) is the value of all goods and services produced in a country or region during a year. It also tells us how big the different markets are in different countries. Some examples (corrected for the respective purchasing powers):

• Finland: 257 GUSD or 49 kUSD per capita (i.e. per person)
• USA: 23 TUSD or 68 kUSD per capita
• China: 26 TUSD or 11 kUSD per capita
• EU: 21 TUSD or 47 kUSD per capita

I am mentioning these numbers as it is quite instructive to know the order of magnitude of these values and how they compare between each other. What is the value normally for a big company? or a state budget? If a company makes 1 GEUR i profit, is that little or a lot for that company? I hope your feeling for big numbers has improved a bit after reading this post.