Waste less time on Facebook — follow Brilliant.
×

Need help! Is there a quick technique?

I encountered the following question. You can brute-force the calculation, but I'm curious to know if there is an easy rule or intuition that I'm missing....

Which is bigger,

100000001/100000002 or
200000001/200000002

Note by Brad Carson
2 weeks, 1 day ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

Hint: If \(a > b> 0 \), then \( \dfrac1a < \dfrac 1b\), and also \( 1 - \dfrac1a > 1 - \dfrac 1b\).

Pi Han Goh - 1 week, 5 days ago

Log in to reply

They are both slightly less than 1. Which is closer to 1?

Jon Haussmann - 2 weeks, 1 day ago

Log in to reply

That's the question!

Brad Carson - 2 weeks, 1 day ago

Log in to reply

If we want to see which is closer to 1, we should compare \[1 - \frac{100000001}{100000002} \quad \text{and} \quad 1 - \frac{200000001}{200000002}.\] What does that give you?

Jon Haussmann - 2 weeks, 1 day ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...