# How to find the ratio of two numbers written in scientific notation, such as $2.69 \cdot 10^{-8}$ and $2.23 \cdot 10^{-7}$?

The numbers are forces and he wants us to put them in a ratio in order to compare them, but I'm really bad at ratios so.

$2.69 \cdot 10^{-8}$ Newtons is obviously smaller than $2.23 \cdot 10^{-7}$ Newtons, but how can that be expressed in a ratio?

• $\left(2.69 \cdot 10^{-8}\right)/\left(2.23 \cdot 10^{-7}\right)$? – user61527 Nov 15 '13 at 2:26
• Is it really that simple? – Paige Nov 15 '13 at 2:26
• If you want a ratio, why not just divide? – user61527 Nov 15 '13 at 2:26
• The scientific notation scared me I guess. I've never been good at math like that, I don't really understand why I chose physics instead of chemistry. – Paige Nov 15 '13 at 2:28
• $\frac{0.0000000269}{0.000000223}$ = $\frac{269}{2230}$ – Steve ODonnell Nov 15 '13 at 2:48

Making this an answer: You would do the same thing with scientific notation that you would do with integers or any other reals. $$\dfrac {a \cdot 10^p}{b \cdot 10^q} = \dfrac {a}{b} \cdot 10^{p-q}.$$Here, we have $$\dfrac {2.69 \cdot 10^{-8}}{2.23 \cdot 10^{-7}} = \dfrac {2.69}{2.23} \cdot 10^{-1} = \dfrac {269}{2230}.$$