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Dividing Decimals

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Dividing Decimals

by AleksandrM » Wed Feb 13, 2008 10:45 am
I searched all over the forum for some good strategies when deviding decimals. The basic answer is one taken from the Princeton Review; namely, to convert both numbers into wholes and then divide. I want to know if there is something else. For example, what would be a quick way to divide the following:

25 / .128

The above numbers are taken from a very simple rate comparison problem, made more difficult due to this final division.

Help would be appreciated.
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by davidforsberg » Thu Feb 14, 2008 1:42 pm
25/0.128 --> multiply the top and bottom by the number of decimals, in this case 3, so you would have --> 25000/128 from then on it's just simple fractions.
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by Stuart@KaplanGMAT » Thu Feb 14, 2008 1:56 pm
Whenever you see weird numbers on the GMAT, there has to be a simpler solution than plugging away at the arithmetic.

As a first step, do what David suggested: eliminate the decimals.

Let's look at the next step:

25000/128

We know this is going to be ugly if we use long division. Instead, let's rewrite it and estimate.

First, let's make the numbers we're using more manageable:

(250 * 100) / 128

I chose those numbers because now the 3 terms are about the same size.

Next, instead of actually solving, let's estimate:

250/125 would be 2. Therefore, 250/128 is a bit less than 2.

So, we have a bit less than 2 * 100 = a bit less than 200.

The ability to see this kind of shortcut on testday will save you a LOT of time. Remember, you don't get any marks for work done (the GMAT is definitely not a grade 9 math test on which you get 1 mark for the right answer and 19 marks for your solution), so quick and dirty is always better than long and elegant.
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Interesing way of looking at it

by AleksandrM » Mon Feb 18, 2008 10:57 am
Wow David and Stuart. That is a very interesting way of looking at that problem. I have tried a few other problems I found to be difficult because of the numbers, and found that I have been able to approximate them relatively quickly using your strategy. Thanks a bunch.
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by humeixia » Thu Apr 10, 2008 2:04 pm
:lol:
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by jeremystaub28 » Tue Apr 02, 2013 7:28 pm
I was having similar problems and I think the best way to estimate these type of divisions is with fractions. In our example 0.128 is very close to 1/8= 0.125, hence 25/(1/8)=25*8=200. Since we slightly reduced the denominator so the result will be a bit smaller than 200. This technique works perfectly when we need to divide by things like 2.5 or 0.66 etc !
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