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When I do calculations I like to round off to say nanometers for wavelength. That means I need it in the form $whatever \times 10^{-9}$. The problem here is that regardless of the number I manage to mess that up in my head. Same goes for large numbers, what is the quick mental math of not messing this up? Examples below.

$50*10^{-8}$ and $60*10^{-10}$
I would like the mental trick to turn both of these into nanometers without my mind drifting off. If you have similar tricks for large numbers, greater then one. Please let me know them! I have an oral practical exam in physics next week and need this, really simple part, to stick!

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up vote 1 down vote accepted

For $50 \times 10^{-8}$, $10^{-8}$ is too $large$, so when you make it smaller, you must make $50$ larger, so $500 \times 10^{-9}$. Conversely, for $60\times 10^{-10}$, $10^{-10}$ is too $small$, so when you make it larger, you must make $60$ smaller, so $6\times 10^{-9}$.

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Ok, so I can think about the ratio. If I make one smaller the other must grow, otherwise the ratio changes and it becomes a different number. Not bad! – Algific May 19 '12 at 13:12

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