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Another large exponent problem

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by Ian Stewart » Sun Jan 25, 2009 2:47 pm
This question asks you to estimate the answer, not find the exact answer. If you look at the numerator, 10^8 is equal to 100 million, while 10^2 is just one hundred. So the numerator is almost exactly equal to 100 million. In the denominator, 10^7 is 10 million, while 10^3 is one thousand, so the denominator is almost exactly equal to 10 million. That is, we'll get an excellent estimate of the fraction's value just by considering the terms with the largest exponents: 10^8/10^7 = 10.
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by cooperbaker » Sun Jan 25, 2009 2:58 pm
Makes sense -- thanks!
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by gaggleofgirls » Sun Jan 25, 2009 5:46 pm
I don't understand how "What is x/y?" is asking us to estimate?

If the question was "x/y is nearest to?" or "x/y equals approximately?" then I would have gotten the estimate part.

-Carrie
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by cooperbaker » Sun Jan 25, 2009 6:07 pm
gaggleofgirls wrote:I don't understand how "What is x/y?" is asking us to estimate?

If the question was "x/y is nearest to?" or "x/y equals approximately?" then I would have gotten the estimate part.

-Carrie
Carrie -- after looking back at the question it did ask to approximate, in my haste to find an answer I just typed out the problem without the proper wording. Sorry for confusion.
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by gaggleofgirls » Sun Jan 25, 2009 6:13 pm
Ah, thank you. With the estimate in the question, then 10 number created by the large exponent (10^8 and 10^7) so dwarf the numbers created byt the small exponents, that they can be discarded and 10^8 / 10^7 = 18^8-7 = 10

-Carrie
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