Let the numbers m, n, p, and s be defined as: m = 0.1212121212... n = 0.1221221221... p = 0.1122112211... s = 0.1112221112... Which choice shows the correct ordering of these numbers?A) m < n < p < s B) s < p < m < n C) n < m < s < p D) p < s < n < m E) s < p < n < m

Accepted Solution

Short Answer: B
The < symbol means that the number on the left is smaller than the number on the right. When I was first stumbling through < or > the point goes to the smallest number and the open end goes to the most generous (largest) number. 

So in this question, the smallest number is on your left, and the largest number is on your right. 

Working it out
Method One
But which number is smallest and which way is biggest? You can get your calculator to tell you the answer. You can subtract one number from the other. Like m and p. Try m - p.
If you get a plus answer m>p
If you get a minus answer m<p
m = 0.12 p = 0.11
m - p = 0.12 - 0.11 = 0.01 and it is positive. 
Conclusion m>p   
Conclusion 2: A and C are both wrong.

Method Two
You can just scan the numbers with your eye and pick out the biggest one.
Start with m. 
It is 0.12 Is there anything bigger?
n is but you have to go to the third decimal place. n = 0.122 m = 0.121 n is bigger than m (and of course p).

So what does that do? Anything?
Yes it picks out the answer. B. Nothing is bigger than n so it should be on the far right. Only B shows that.