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Yes, "half again" clearly means 150% of the original. I think the dearth of equivalents is simply because saying something like "three quarters again" is more easily expressed as "an increase of 75%." By comparison, "half again" seems easier.
I do see some confusion online regarding percentage changes. Not so much in print. Like if something changes from 40 units to 50 units, is that a 10/40 = 25% increase, or is it a (50-40)/50 = 20% increase? Convention favors the former, but I see it done both ways.
Heimhenge said
I do see some confusion online regarding percentage changes. Not so much in print. Like if something changes from 40 units to 50 units, is that a 10/40 = 25% increase, or is it a (50-40)/50 = 20% increase? Convention favors the former, but I see it done both ways.
There certainly is confusion in percentages, mainly with accounting terms. Your example shows a 25% increase (or markup) and a 20% profit. People seem to interchange increase and profit without much thought. If you have seen people who call your example a 20% increase, they were wrong.
Often newspaper stories have people saying "We reduced our costs by 200%" which is clearly not what happened.
When there costs drop from $200 to $100, that's 50% less, but a lot of people claim that a drop from $150 to $100 is a 50% reduction. At one time, I thought such people were deliberately lying, and I suppose some are, but mostly, I think they are simply fools who ought not be trusted with a checking account.
Percentage reductions can be a little tricky depending on how they're expressed. For example, if you say:
1. Cost was reduced TO 30%.
or
2. Cost was reduced BY 30%.
you clearly have two totally different meanings. Substitute "100%" in either of those examples and you have gibberish. Substitute "50%" and you have equivalent statements. I think most of the confusion comes from ignoring the rule that the original amount is supposed to be used as the base (divisor) for expressing the change.
Thus, if the change is from 100 to 80, that's a drop of 20, so it's a 20/100 = 20% reduction. But what I often see is people figuring that same drop as 20/80 = 25%.
For the same reason, a doubling of cost is a 100% increase, not the 200% I often hear cited.
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