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by illini1980 » Wed Jun 17, 2009 5:10 pm
I am struggling with easy/simple questions such as the following. I am taking too long to answer them. Any short cut help?

10^8 - 10^2 / 10^7 - 10^3

a) 1

b) 10

c) 10^2

d) 10^3

e) 10^4

There has to be a quick and simple way. Thanks!
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by raleigh » Wed Jun 17, 2009 6:25 pm
Did you write this problem incorrectly? Should there be paranethesis or anything? I approximate this to be 10^7.
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by illini1980 » Thu Jun 18, 2009 4:55 am
Here is the edited version. Sorry about that:

(10^8 - 10^2) / (10^7 - 10^3)

a) 1

b) 10

c) 10^2

d) 10^3

e) 10^4
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by raleigh » Thu Jun 18, 2009 8:24 am
The question says approximately, right?

Since each term is base 10, we can factor the numerator and the denominator. Since it's addition/subtraction we have no other way of combining terms.

Numerator: (10^8 - 10^2) = 10^2(10^6-1)

Denominator: (10^7 - 10^3) = 10^3(10^4-1)

So (10^8 - 10^2) / (10^7 - 10^3) =

10^2(10^6 - 1)
_____________ =
10^3(10^4 - 1)

(10^6 - 1)
_____________ =
10(10^4 - 1)

99999
______ but this isn't an answer so they must want an approximation.
9990

That's messy, but we can approximate 10 from it. It's easier to look at it like this: 10^6 - 1 = 99999 which is close enough to 10^6 = 100000 for an approximation. Similarly, 10^4 is close enough to 10^4 - 1 for an approximation. Using these approximations:

(10^6 - 1)
_____________ ~ 10^6/(10*10^4) = 10^6/10^5 = 10.
10(10^4 - 1)
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by illini1980 » Thu Jun 18, 2009 11:24 am
Yes, it states approximately. Thanks!
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by raleigh » Thu Jun 18, 2009 11:53 am
You're welcome. Please take the time to write out the exact question so everything is clear to the people helping.
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by kevincanspain » Thu Jun 18, 2009 1:17 pm
Realize that the numerator is practically 10^8 and the denominator is practically 10^7. The quotient is practically 10

If you have 10,000,000 dollars and spend 100, you have about 10,000,000 dollars left.

It is important to look at the answer choices before you begin working!
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