Dividing Decimals

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AleksandrM: Legendary Member; Posts: 566; Joined: Fri Jan 04, 2008 11:01 am; Location: Philadelphia; Thanked: 31 times; GMAT Score:640

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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Source: Beat The GMAT — Problem Solving | Wed Feb 13, 2008 10:45 am

davidforsberg: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Tue Feb 05, 2008 10:47 am; Thanked: 3 times

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.

T minus 17 hours

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

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.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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AleksandrM: Legendary Member; Posts: 566; Joined: Fri Jan 04, 2008 11:01 am; Location: Philadelphia; Thanked: 31 times; GMAT Score:640

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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humeixia: Junior | Next Rank: 30 Posts; Posts: 27; Joined: Thu Apr 10, 2008 1:20 pm; Thanked: 1 times

by humeixia » Thu Apr 10, 2008 2:04 pm

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jeremystaub28: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Fri Sep 09, 2011 9:23 am; Thanked: 1 times

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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