how do you simplify obnoxious fractions and decimals easily?

[mrh125]

like say you have something like 1/(2.5*10^(-3)), 35/47, or how would you quickly estimate or simplify that or 1/.0658 or something? Also, anything with square roots(i memorized sqrt(2) and sqrt(4) values). I need to be able to roughly estimate obnoxious numbers and do calculations quickly

There seems to be a lot of obnoxious stuff like that that may appear on the mcat. I've been rounding and doing fast multiplication but it's still annoying to do stuff like this.

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[Lifeman]

• When you are multiplying or dividing something in scientific notation, put both terms in scientific notation. You can multiply or divide the beginning numbers, and then add or subtract the exponents for multiplication or division. So for your example you would do, 1x1o^0 / 2.5x10^-3 which gives you (1/2.5) x 10^(0--3).
• Then for fractions, try to get the denominator to 10 or 100 or something. So for the same example of 1/2.5, if you multiply the top and bottom by 4, you get 4/10, so you just move the decimal on 4.0 to the left once. For 35/47, if you multiply top and bottom by 2, you get 70/94. Move the decimal to the left of 70.0 by two and you get 0.70, and since the bottom is a little smaller than 100, your answer will be a little bigger than 0.70
• For square roots, you can either find squares around the number and estimate, or split up the number into squares. So for the square root of 52, we know 7^2 is 49 and 8^2 is 56 so our answer is between 7 and 8. The other way is to split it up. So 52 = 2 x 36 = 2 x 6 x 6. So our answer is 6 x sqrt (2)

 

[Odi]

I have a tendency to turn all my numbers into scientific notation. If you practice enough you'll get very quick at it.

For 35/47 I would quickly do 350 x 10^-1 / 47

This way my numerator is bigger and I can handle the problem much much easier. 350 divided by ~50 is 7. My scientific notation part becomes -1 - 0 = -1. Answer is 7 x 10^-1 ~ 0.7

This may seem longer at first but it's simply shifting decimal points to the left or right making any number bigger or smaller so they're easily manageable and then it's just your basic addition or subtraction for your powers. I've become extremely efficient at estimating answers with this and now I love seeing scientific notation. I don't know if this method is good for everyone.