Hey SFtraveler:

On the GMAT the easiest way to calculate using decimals is to not use decimals at all!

I'd multiply the numerator and denominator to get rid of the decimals in the denominator. To do that, you need to move that decimal place over three spaces to the right, so you have to multiply by 10 three times. That leaves:

20(.0003)/2 (I'll just stick to multiplying the common 2 term by 10 so that it stays simple)

Now the twos cancel, so you have:

10 * .0003

You can then move the decimal place once over to the right with that remaining 10, so you get:

.003

Generally speaking, when you see decimals, do whatever you can to turn them into fractions or integers. If you have place values preceded by a 0, you can multiply by 10 to get rid of the zeroes (either do the same to the top and bottom of a fraction to keep the value the same, or the same to both sides of an equation to keep the equation the same); if you have a term like .3333, convert that decimal to the fraction 1/3 so that you can work with the 1 and the 3 instead of a long, repeating decimal.

Decimals are great for use with calculators...but the brain (and the pen) works best with integers.

Thanks for your response Brian. So you don't have to multiply the (.0003) by 10 also...you can just isolate and multiply the (.02) by 10?

Hey SF:

(first, congratulations to SF on the World Series last night!)

Not only do you "not have to" multiply .0003 by 10 also, you CANNOT do it.

What we're doing when multiplying the numerator and denominator by 10 is essentially just multiplying the whole fraction by 1. 10/10 = 1, but strategically having those 10s allows us to move the decimal points. What we really have is:

1000(.02)(.0003)/1000(.002)

We add the 1000/1000 to move the decimal points, but we can only do it once to each the numerator and denominator - if we do it twice to the top and once to the bottom, we're no longer multiplying by 1 and therefore we're violating the rules of algebra.

From there, with the "2" terms, that in the numerator only has two decimal places to move while the denominator has 3, so that's why we end up with 20 on top, to carry the extra multiple of 10:

20(.0003)/2

10(.0003)

.003

I hope that helps...

I thought so, but helps having your verification of it.

And yes, the city of SF is enjoying the Series win...it's been a long time coming.

SFtraveler wrote:What is the quickest way to solve (.02)(.0003)/(.002) using cancelling?

0.02 x 0.0003 = 6 x 10^(-6) the power can be found by counting the number of digits after the decimal points. (-) sign indicates that the numbers are in decimal.

0.002 = 2 x 10^-3

Now 6 x 10^(-6) / 2 x 10^(-3) = 3 x (10^(-6)) / 10 ^(-3))


Remember a^n/a^m = a^(n-m)

so the answer is 3 x 10^(-3)
which is 0.003
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