# What would the correct English description be for the difference for 1/3

If you measure a task & it takes 3 seconds, then the next time you do the same task, it takes you 1 second, is the difference 200% or 67%?

Or would you say the difference is 200% because 3-1=2 or 200% better -- but the percentage of difference is 2/3 or 67%? I'm pretty sure I'm confusing something if not someone. Be that as it may, I need to explain this clearly so that the analysis is clear & credible. The example I would site would be: Let's say you are mesuring system transaction response times & on two separate tests find the response time improvement noted. (Thanks PH)

• It was done in one third the time or three times the speed. Commented Mar 31, 2015 at 0:14

For maximum clarity, I would simply say "The time per task improved from three seconds to one second". If you desire to use percentages, percentage change is expressed as $\frac{\text{new}-\text{old}}{\text{old}}$. So you could say "The time per task decreased $66\frac{2}{3}\%$, from 3 seconds to 1".
Assuming the task is being performed continuously, you could instead measure tasks completed per unit time, which has improved from $\frac{\text{time}}{3}$ to $\frac{\text{time}}{1}$, a $\frac{\text{time}-\text{time}/3}{\text{time}/3}=\frac{2(\text{time})/3}{\text{time}/3}=2=200\%$ improvement.