Methods to quickly compute percentages

Question

Yesterday, talking with a friend of mine, she asked me what is a quick (and – of course – correct) way to compute percentages, say $3.7 \%$ of $149$. Frankly, I was sort of dumbfounded, because I use the following two methods:

• either I use ratios,

• or I start to go on with a sequence of approximations (e.g. I get the $10$% of $149$ and then I proceed by roughly converging towards $4$%, and then I wildly guess...).

In both cases, she was not satisfied: ratios were too slow, and the other system... well, you can guess by yourself.

Are there some other options that are both fast (which means that you should not need pencil and paper to make the calculation) and sound?

Please, notice that I am not interested in the result of the example I chose itself: this should rather be a way to show a particular system.

Thank you for your time.

PS: To the moderators, I was seriously contemplating the idea of using the tag "big list", but I am not sure the topic is that compelling.

Answer 1

3.7% of 100 = 3.7

3.7% of 40 = 4*0.37 = 1.48

3.7% of 9 = 9*0.037 = 0.333

3.7+1.48+0.333=5.513

Answer 2

I use to evaluate the $1\%$, in your case $1.49$ and multiply for the given percentage: $1.49 \times 3.7$. it is only one multiplication that, if I'm not interesting to exact value I can evaluate approximating the numbers saying that the value is something between $3.5\times 1.5=5.25$ and $4 \times 1.4 = 5.6$.