Silly fraction question

[SSerenity]

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Hey team,

I'm working through Gen Chem. I came across this problem several times before in physics too.

My problem boiled down to recognizing that

228/760 = 3/10 = 0.3

I can't for the life of me arrive at this conclusion without spending a ridiculous amount of time.

What I've been doing was testing ratios of 1/2, 1/3, 1/4, 1/5 etc. and picking the one that looks like it would be the closest. This is also time consuming. But when the numerator is 3 like in this example, I would realistically never go any further.

How do you guys quickly simplify fractions like these?

 

[UCFMD]

I'd round 228 to 230 and make it 23/76.

Which is pretty close to one third.

 

[dcamkl1]

You could rewrite it as:

(22.8 x 10) / (7.6 x 10^2) = ~ 3 x 10^-1 = 0.3 ish.

And hopefully the answer choices are varied enough for you to pick the closest one.