Mathematics
Large numbers
Thousand, million, billion: read, compare and size up numbers with lots of zeros.
In a single evening of news you hear 84 million inhabitants, a budget of 500 billion euros and 150 million kilometres to the sun. The words sound similar, yet the sizes behind them are worlds apart. Anyone who reads such numbers confidently can tell at once whether a figure is enormous or rather modest. That is exactly what you learn here: group, read, compare.
Groups of three from the right
Nobody can read a string of digits like 1204583 at a glance. That is why large numbers are grouped in blocks of three digits, always from right to left: 1,204,583. English uses a comma for this, German uses a point or a thin space, so the same number appears as 1.204.583. Careful: this separator is not a decimal point, it only sorts the digits and makes the number neither bigger nor smaller. Why start from the right? Because the groups begin at the ones. So the group on the far left may well hold only one or two digits, as in 45,900.
Every group has a name
From right to left the groups are called ones, thousands, millions and billions. That is what makes grouping so useful: you read each block of three as an ordinary three digit number and add the name of the group. So 24,500,000 becomes 24 millions, 500 thousands and 0 ones, spoken as twenty four million five hundred thousand. Never drop the zeros inside a group, they hold the places open: 7,030,000 is seven million thirty thousand, not seven million three thousand. One trap when translating: the English billion is the German Milliarde.
Each step on the scale means ten times bigger.
How much more is a million?
Thousand and million sound alike, but they are worlds apart. Time makes the gap easiest to feel: 1000 seconds are barely 17 minutes, about a coffee break. A million seconds are a good 11 days, and a billion seconds are roughly 32 years, half a lifetime. Between two group names there is always a factor of 1000, and that factor hits hard: a sheet of paper is about 0.1 mm thick, so a thousand sheets make a stack of 10 cm and a million sheets a tower of 100 m.
With anchors like these you can place any number you meet in the news. A village has about a thousand inhabitants, a big city like Berlin around 3.9 million, so almost 4 million, all of Germany about 84 million, and roughly 8 billion people live on Earth. A national budget runs to a few hundred billion euros, and the sun is roughly 150 million kilometres away. To compare, count the groups first: 1,200,000 has three groups, 987,654 only two, so the first number wins even though it starts with a small 1. Only when the group count is equal do you read on from left to right.
Exercises
0 of 6 solvedTime to try it yourself. You can't break anything, every attempt counts.
How many digits does a full group hold when large numbers are grouped?
How many digits does one million have when you write it in digits?
How do you write four million twenty thousand in digits?
The number 7,030,000 reads as seven million ….
Write as a number: 3 million 250 thousand.
Match each quantity to the size that fits.