gmontalvo wrote:
I've run across several variants of the following question:
\(\frac{10^8 - 10^2}{10^7 - 10^3}\)
Here is the approach I want to take:
\(\frac{10^2(10^6 - 1)}{10^3(10^4 - 1)}\)
But when I cancel the numerator/demoninator what I am left with is kind of ugly.
\(\frac{999999}{99990}\)
Is there something I am missing? Is there a better way? Or should I just suck it up and do the division?
This is how I would do it:
Factorise the numerator and denominator
\(\frac{10^2(10^6 - 1)}{10^2(10^5 - 10)}\)
Cancel, and you get
\(\frac{(10^6 - 1)}{(10^5 - 10)}\)
Now, some approximation:
\(\frac{(10^6 - 1)}{(10^5 - 10)} \approx \frac{10^6}{10^5}\)
This gives 10. The great part is that you are dealing with such large numbers, that 1 and 10 are immaterial.
The point here is not accuracy, it is to get a sense of what is right or wrong. If you find you have to do long division, then you are definitely missing a trick. Even if a question seems fiendish, there is always a shortcut to the solution!
Hope this helps.
EDIT: Scrolled through Bunuel's post, who has hit the nail on the head