Percentages

[Futsal1st]

I have an object that 17.2 units. Is a part that is 8 units of the 17.2 said to be 300% less or 63% less.

Same objects. If I wanted an object to be 17.2 in size and got a size 8 would you now say the smaller one was a 300% shortfall. My gut says to describe it as a shortfall of 63%.

To me a 300% shortfall sounds wrong. Can you have a 300% shortfall on something?

Thanks in advance for your help.

Confused

 

[tkhunny]

A reduction of 100% means zero (0).

A reduction of 200% has no meaning for a real device or process.

Suppose it normally takes 1 hour to get to grandmother's house.

If we figure a way to get to Grammy's in ½hour, that is a 50% reduction in time and it MAY be a 100% increase in speed. A different route may have been the difference, or part of the difference.

If we figure a way to see our beloved Oma (German, not Korean) instantaneously, that is a 100% reduction in time and it is hard to imagine how that translates to a percentage increase in speed. Some may attempt to call this an infinite increase in speed, but this really is unsatisfactory.

If we figure a way to get to grandmother's house 1 hour before we actually leave, not THAT is a 200% reduction in time. It's not clear at all what would be the related increase in speed.

Now, if you wish to talk about an exchange system of some sort, such as money or assets vs. credit or debt, then we could talk about a 300% decrease, since negative values are quite acceptable mathematically.

Did I elucidate or obfuscate?

 

[JeffM]

I have an object that 17.2 units. Is a part that is 8 units of the 17.2 said to be 300% less or 63% less.

Same objects. If I wanted an object to be 17.2 in size and got a size 8 would you now say the smaller one was a 300% shortfall. My gut says to describe it as a shortfall of 63%.

To me a 300% shortfall sounds wrong. Can you have a 300% shortfall on something?

Thanks in advance for your help.

Confused

Start with tkhunny's point. Real physical objects cannot experience a decrease greater than 100%: a decrease of 100% takes something to zero. However, relative measurements can experience a decrease greater than 100%. If the temperature is at 15 degrees and decreases by 300%, the temperature drops to minus 30 degrees.

But where in the world are you getting either 300% or 63%. Neither is correct.

 

[Futsal1st]

Should be 54.3%, yes?

 

[JeffM]

Should be 54.3%, yes?

Exactly so long as you say "decrease." If you say change, you must say \(\displaystyle - 54.3\%.\)

The formula for percentage change from a base value is \(\displaystyle 100 * \left(\dfrac{changed\ value}{base\ value} - 1\right).\)

 

[Futsal1st]

Thanks every one for your help. Its been a long time since I played with percentages and the other guy had me confused with his 300% decrease.


Cheers