Large numbers

 

These notes deal with space and time. The first thing we notice about the universe around us is how big it is. In order to quantify things in cosmology very large numbers are required and the endless writing of zeroes quickly becomes tedious. Thus people invented what is called the scientific notation which is a way of avoiding writing many zeroes. For example the quantity `one million' can be written as 1,000,000 which is a one followed by six zeroes, this is abbreviated as 10⁶ (the little number above the zero is called the exponent and denotes the number of zeroes after the one). In this way we have

one million=1,000,000=10⁶

one billion=1,000,000,000=10⁹

one trillion=1,000,000,000,000=10¹², etc.

So much for large numbers. There is a similar short-hand for small numbers, the only difference is that the exponent has a minus sign in front:

one tenth=0.1=10^-1

one thousandth=0.001=10^-3

one millionth=0.000001=10^-6, etc.

In order to get several times the above quantities one multiplies by ordinary numbers, so, for example, 8×10⁶= eight millions, 4×10^-12=four trillionths, etc.

This notation is a vast improvement also on the one devised by the Romans, and which was used up until the Renaissance. For example, our galaxy, the Milky Way, has a diameter of about 10⁵ light years (a light year is the distance light travels in one year), in Roman numerals

$$\begin{eqnarray} \html{eqn2}10^5 = && MMMMMMMMMMMMMMMMMMMM \nonumber \\ && MMMMM... ...MMMMMMMMMMMMMMMMMMM \nonumber \\ && MMMMMMMMMMMMMMMMMMMM \nonumber\end{eqnarray}$$

The Andromeda galaxy is about 2×10⁶ (two million) light years from our galaxy, in Roman numerals writing this distance requires 40 lines.