Q:

Calculate time needed to solve problem

I have this question in an assignment and I was wondering if I could get help verifying whether my approach to this question is correct... The question is as follow:

Suppose that an algorithm uses 5n^2 + 3^n bit operations to solve a
  problem of size n. Suppose that your machine can perform one bit
  operation in 10^-9 seconds. How long does it take your algorithm to
  solve a problem of the sizes given below. Note, if your algorithm
  takes more than 60 seconds, answer in minutes. For more than 60
  minutes, answer in hours. For more than 24 hours, answer in days. For
  more than 365 days, answer in years. For more than 100 years, answer
  in centuries!

Let's assume n is 10...
Would I, 
1)Solve for 5(10)^2 + 3^(10)
2) Divide the number of bit operations by 10^-9 to find the answer represented in seconds
3)Divide by minutes or hours or days and so on as needed to find proper representation?
Thanks in advance for any input 

A:

You would
1) calculate $5\cdot 10^2+3^{10}$-you solve equations but calculate expressions
2) multiply by $10^{-9}\frac {\text {seconds}}{\text { bit operation}}$ to get seconds-dividing gives an error of $10^{18}$  If you write out the units you will get it right
3) divide by the appropriate conversion factor-you don't divide by minutes.  You are actually multiplying by $1$ in the form $\frac {1 \text { minute}}{60 \text { seconds}}$ or whichever is appropriate 
Your basic approach is correct, but the writeup is not

