Big NumbersHow high can you count? Could you count to a million? How about a billion? How high you count if you really wanted to? Let's find out.
couldWe'll assume that you can count one number every second. (This sounds realistic, until you remember that after a while you'll have to say 'three million, six hundred eighty seven thousand, eight hundred fifty seven' in one second. However, for convenience we'll assume you can do it).
We'll also assume that you can count every second of every day (in 24 hours that's 84,400 seconds). So it would take you exactly one day to count to 86,400. With us so far? The table below shows how long it would take you, counting continuously at one number per second, 24 hours per day, to reach various big numbers...
Larger numbers include sextillion (10^{21}), septillion (10^{24}), octillion (10^{24}), etc. The Earth has a mass of 6 octillion grams.
You could probably count to one thousand. It only takes about 17 minutes; you may even have done it as a child. But it's clear that you'll never make one million, let alone one billion, and not just because you'll get bored. You can't go for 12 days without sleep, and certainly not 32 years! Let's be a little more realistic and assume you devote a full 8 hour work day to the job of counting. In 8 hours there are 28,800 seconds, so after your first day on the job you'll have reached 'twenty eight thousand eight hundred'. At this more realistic rate of counting, it will take three times as long to count to where you want to (8 hours is a third of a day), and assuming you report for work every day, seven days a week, it will take you about 36 days to reach one million. You could do this if you really wanted to. How about one billion? Could you count to a billion if you wanted to? Well, that would take you about 96 years ... you won't live long enough! It's impossible to count to one billion!
You may have noticed the column in the table above labelled 'Scientific Notation'. You'll learn about this in Math 9, and use it a lot in Sr. High math and science classes. This provides a convenient way of representing big numbers so we don't have to use all those zeros. One million, or
^{6}, or 1 x 10^{6}.Small NumbersLet's use distances this time to make the size of these numbers more understandable. We'll work in metres. One tenth of a metre is a decimetre, or 10^{-1} m. This is 10 centimetres, or about the width of your hand.
One hundredth of a metre is a centimetre, or 10^{-2} m. This is 10 millimetres, or about the width of a fingertip.
One thousandth of a metre is a millimetre, or 10^{-3} m. This is a tenth of a centimetre, or the width of a pencil lead.
After this point it's much more difficult to visualize sizes...
One millionth of a metre is a micrometre, or 10^{-6} m. A strand of human hair is about 100 micrometres wide. Red blood cells are 7 micrometres in diameter. You'll need a microscope to see anything that's just a few micrometres in width.
One billionth of a metre is a nanometre, or 10^{-9} m. A DNA molecule is 2 nanometres wide. Ten hydrogen atoms side by side are 1 nanometre long. This distance is so tiny that things this long can't even be seen in a regular microscope!
One trillionth of a metre is a picometre, or 10^{-12} m. Atoms are typically between 60 and 600 picometres in diameter.
Again you'll notice we showed these tiny numbers using scientific notation, only this time they were written using negative exponents. For example,
10 means 'one over 10^{-3}^{3}, or 'one thousandth', or 0.001 ... you can learn more about negative exponents here. |