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In summary, an increase of 400% on "x" would be expressed as 5x according to mathematical convention. However, some may interpret it as 4x due to conventions in other industries such as clothing stores. This confusion can also be seen in gambling, where odds of 3 to 1 are expressed differently than odds of 5 for 1. Ultimately, the interpretation may vary depending on the context and industry.
- #1
Holocene
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If "x" is to be increased by 400%, is that expressed as 4x or 5x?
If "x" is to be increased by 400%, is that expressed as 4x or 5x?
Thanks.
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- #2
berkeman
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It can be open to interpretation, but I believe that the mathematical convention (as opposed to the clothing store convention) would be:
An increase in x by 400% means that you now have 100% of x plus 400% of x (the increase is the 400% on top of the initial 100%). So you have 5x after that increase.
- #3
robert Ihnot
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The basic fact is that if X is increased by 100%, that can not be X, it must be 2X. This leads to a 400% increase results in 5X.
However, as berkeman points out, not everybody sees it that way. If someone offers you 500% on your investment, you'd might have to ask if that means to return 5X or 6X, since these kind of figures are put out without much thinking going on.
A reason for this confusion is, for example, in dice of being paid odds of 1-1, which obviously mean returning 2X. So that if odds in dice are 5 TO one, the return is 6X. But if the matter is expressed as 5 FOR 1, then the return is 5X.
There is some logic in this because if in dice the payoff is 3 to 1, then the dealer places three stacks of chips next to your stack on the table when you win, and you take all.
But take the matter of a video poker machine. If the payoff is 9 for a Full House, this means you get nine coins back on playing one coin. The original investment is expended at once and is thought of as the property of house. This situation leads to the amazing fact as one writer saw it, that if you win 1, then lucky you! investing one coin, you are now a "winner;" you got your own coin back! )
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1. Is increasing by 400% the same as multiplying by 4?
Yes, increasing by 400% is equivalent to multiplying by 4. This means that the new value will be four times greater than the original value.
2. Why is it not expressed as 5x?
It is not expressed as 5x because the 400% increase is based on the original value of x. If we were to express it as 5x, it would imply that the original value of x is already included in the increase, which is not the case.
3. Can the increase be expressed as 400x?
No, the increase cannot be expressed as 400x. This would imply that the new value is 400 times greater than the original value, which is not correct. Multiplying by 400% is equivalent to multiplying by 4, not 400.
4. How is 400% increase different from a 400% decrease?
A 400% increase means that the new value is four times greater than the original value. On the other hand, a 400% decrease means that the new value is four times smaller than the original value. This can also be expressed as multiplying by 0.25 or dividing by 4.
5. Is there a more accurate way to express a 400% increase?
Yes, a more accurate way to express a 400% increase is to use the decimal form of the percentage, which is 4. This means that the new value is 4 times greater than the original value. However, both 4x and 400% are correct ways to express the increase.
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