Estimation of decimals in fractions

[alexisvargas85]

I have a question in the Fractions, Decimals & Percents Strategy Guide, Manhattan PREP, fifth edition.
In the page 120, the problem of the Chapter 7 says: Estimate the following fractions in terms of decimals, and...
To estimate the fraction 14/90 I simplified the fraction to 7/45 and I increase the denominator to 49 to simplify again and I got 1/7, but in the solution they increase the denominator to 100 and the result is 0.14 o 7/50. I do not understand why the steps I followed were wrong since I did the steps explained in the chapter, could you guys explain me what is wrong?
Thank you,
Alexis

[RonPurewal]

Hi Alexis,
Could you please post the full text of the problem (and, if appropriate, the parts of the solution that you're quoting)? We don't always have access to the guides when we are posting -- and we'd like to create threads that will be useful to other readers of the forum.

Thank you.

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From what you've posted here, I can make three comments:

1/
Estimation is ... well, estimation, so there's not going to be one correct answer (unless you are given specific instructions, such as "round to the nearest tenth"). So there's nothing wrong with getting an answer that's different from ours.

2/
Remember that the end goal of the problem is to produce a DECIMAL approximation.
The fraction 1/7 is pretty awful in decimal form (it's 0.142857142857...); in other words, not the most beautiful -- or useful -- decimal approximation in the world.

3/
45 is closer to 42 than to 49, so, if you're going to go that route, you should probably round to 7/42 = 1/6 to produce a better estimate.
Or you could get the same estimate by rounding 14 to 15, which would give you 15/90 = also 1/6.