   SEARCH HOME Math Central Quandaries & Queries  Question from Ammara: Hi, I'm trying to figure out how a paper I'm looking at has found a percentage from the numbers below. its a paper comparing two lenses. it says that the new lenses 'slowed the progression of refractive error by approximately 50%'. the refractive error with the old lenses was -2.26 after two years it was -3.28 the refractive error with the new lenses was -2.24 after two years the refractive error is - 2.75 Thank you so much for your help it is most appreciated! Hi Ammara,

The method for calculating percentage change is described in our response to an earlier question.

For the old lenses I think that in the paper you are reading they take the earlier measurement to be 2.26 and the later to be 3.28 so the calculation is

$\frac{3.28 - 2.26}{2.26} = \frac{1.02}{2.26} = 0.4513 \mbox{ or } 45.13 \%.$

For the new lens the calculation gives

$\frac{2.75 - 2.24}{2.26} = \frac{0.51}{2.26} = 0.2377 \mbox{ or } 23.77 \%.$

Since 23.77% is approximately one half of 45.13% I think the authors feel they can say that "the new lenses 'slowed the progression of refractive error by approximately 50%'".

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.