A Question of Scale

Age 14 to 16 Challenge Level:

'Order of magnitude' in science is a very useful concept: we are often not necessarily interested in the exact measurement of a quantity but rather whether it is 'about a metre' or 'about a kilometre' or 'about a nanometre' etc.

Orders of magnitude makes the use of scientific notation. For any two numbers $X$ and $Y$ we use the notation $X$e$Y$ to mean $X\times 10^Y$. In case you are wondering, the letter $e$ stands for 'exponent' and is sometimes written $E$ instead. In standard notation, the number $X$ must be between $1.0$ and $9.99...$ and the exponent a whole number.

For example, $1.2$e$3$ is $1.2\times 10^{3}$, which is the same as $1200$.

The power of $10$ can also be negative, so that $6.8$e$-2$ means $6.8\times 10^{-2}$, which is the same as $0.068$.

In science, certain exponents are more frequently used. Powers of $\pm 3,\pm 6, \pm 9, \pm 12$ are standards, which is why you will see (non-standard) measurements such as $375$e$-9$m, which scientists would refer to 'Three hundred and Seventy Five Nanometres'. You will need to convert such numbers to standard form before placing them on the scale.

Are there any objects whose size you are confident you know? Are the other objects larger or smaller than these?