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(10^8 - 10^2) / (10^7 - 10 ^3) is closest to 10?

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(10^8 - 10^2) / (10^7 - 10 ^3) is closest to 10?

by canuckclint » Sat Sep 13, 2008 12:47 pm
why?
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by mals24 » Sat Sep 13, 2008 2:12 pm
(10^8-10^2)/(10^7-10^3)

take out 10^2 and 10^3 common from the num and den

[10^2(10^6-1)]/[10^3(10^4-1)]

Simplify the fraction by dividing 10^2/10^3 you get

(10^6-1)/[10(10^4-1)]

Now 10^6-1 is approx = 10^6
and 10^4-1 is approx = 10^4

So we get

(10^6)/[10(10^4)]
=(10^6)/(10^5)
=10
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by jcbruin » Mon May 31, 2010 7:47 pm
mals24 wrote:(10^8-10^2)/(10^7-10^3)

take out 10^2 and 10^3 common from the num and den

[10^2(10^6-1)]/[10^3(10^4-1)]

Simplify the fraction by dividing 10^2/10^3 you get

(10^6-1)/[10(10^4-1)]

Now 10^6-1 is approx = 10^6
and 10^4-1 is approx = 10^4

So we get

(10^6)/[10(10^4)]
=(10^6)/(10^5)
=10
Thanks for the explanation. I factored out 10^2 in the numerator and 10^3 in the denominator but should have estimated/approximated! :shock:
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by Testluv » Tue Jun 01, 2010 1:40 am
10^8 is super-super big relative to 10^2.

So 10^8 - 10^2 will be very close to 10^8.

Likewise, 10^7 - 10^3 will be very close to 10^7.

So the question becomes:

what is 10^8/10^7 close to?

Clearly, it is close to 10.
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by azarmij » Thu Jun 03, 2010 10:31 pm
Could you please explain why 10^8 is super-super big relative to 10^2.?!

I only can think that this is far to each other..

thanks
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by uwhusky » Thu Jun 03, 2010 10:36 pm
10^8 = 100,000,000 comparing to 10^2 = 100.

Maybe you need little more focus on exponents.
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by azarmij » Thu Jun 03, 2010 10:50 pm
Maybe the way I asked wasnt as clear,

I know 10^8 is super big comparing to 10^2. I didnt know why you just delete 10^2 but I guess even when you minus 10^2 from 10^8 it is still close to 10^8, is that why you just delete 10^2 and leave 10^8?
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by papgust » Thu Jun 03, 2010 10:55 pm
Since the question asks only for an approximate answer, yes you ignore 10^2. However, if the question asks for an exact answer, don't approximate!
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by azarmij » Thu Jun 03, 2010 11:08 pm
Got it..! thanks alot
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by kevincanspain » Fri Jun 04, 2010 12:44 am
Jose had $100,000,000 and gave $100 to charity. Luis had $10,000,000 and gave $1,000 to charity. After their charitable giving, approximately how many times as much money as Luis did Jose have ?
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by ganesh prasath » Thu May 26, 2011 2:29 am
But for the above problem 10^2 seems to be the most obvious sol ..why is it 10 instead?
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by amar66 » Thu May 26, 2011 11:13 am
Take 10^2 common from Nr. & 10^3 from the Dr.--> 10^2(10^6-1)/10^3(10^4-1)
(10^6-1) approx = 10^6 and (10^4-1) approx= 10^4

so the fraction reduces to (10^6)/10(10^4)=10 & It is the answer
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