Quick mental math techniques?

Question

I am taking a timed standardized test shortly (MCAT), it is very chemistry and physics heavy. The calculations are not difficult, but I am not allowed a calculator and I need to think very quickly. I was wondering if anyone has any tips or ways to "think" about a problem for quick mental math. I'll give a couple examples: something like
(0.30/8) or (1200/0.6) or (.9)^3 or (.30)^.5 My problem in mainly in thinking about decimal divisions and squares QUICKLY.

great answers so far, I should have mentioned I only need to "estimate" as the multiple choice responses are generally rounded.

Answer 1

Here are quick ways to do each fo the problems you typed.

0.30 /8 = 30/8 * 1/100 = 3.75/100 = 0.0375

1200/0.6 = 12000/6 = 2000

0.9^3 = (9/10)^3 = 729/1000 = 0.729

(0.3)^0.5 = sqrt(30/100) = sqrt(30) / 10 ~ = 5.something / 10
= 0.5something

Answer 2

Looks like simple arithmetic. Most of them don't require a calculator
0.3/8 is 1/10 of 3/8. 3/8=.375. So 0.30/8 = .0375 (I know my decimal equivalents for fractions with denominators 2, 3, 4, 5, 6, 7, 8, and 9)
1200/0.6=10*1200/6=10*200=2000
.9^3 = [(1/10)^3][9^3] = 729/1000 = 0.729

But, if a calculator is allowed, I'd go to the calculator for the last one. Square roots are non trivial if they're not obvious. And the square roots or 3 and 10 are irrational.

Answer 3

Try thinking of the decimal and the number separately.

For example, .30/8 = 3/8 * 1/10, so if you know that 1/8 = .125, then 3/8 = .375, and .3/8 = .0375.

1200/.6 = 1200/6 /10 = (1200/6) * 10 = 200 * 10 = 2000.

.9^3 = 9^3 * (1/10)^3 = 729/1000 = .729

.30 ^ .5 is a bit trickier, because raising something to a number between 0 and 1 is actually taking a root of it. x^(1/2) = sqrt(x). In this case, sqrt(.30) = something between .5 and .6, just as sqrt(30) = something between 5 and 6.

Answer 4

On a division:remove the decimal and add zeros to a none decimal number then divide. when you finished put the decimal back to the result, number must be smaller than the original. On multification, multiply as of the decimal does not exist when you done then plug the decimal back to the number and it has to be larger that the original. to remember things during the exam, now look at the roof of you leaving room an with one eye twisted to left and count how many windows are in your houss and then do same thing to right eye and find out which side is faster and more correct. that is where your brain stores information's. It will work.

Answer 5

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Answer 6

Try to see decimals as number multiplied by 10^-n

for example, 0.06 will be 6 * 10^-2

This way your calculations will be much more easy. Also bring plenty of scrath paper.

Answer 7

one word:FOCUS

and do not frustrate!!