# How much exactly is increased when it is “increased by 1.1”?

I saw it in a text book, and a similar problem that also appeared in the book is "3 times faster", which is already asked. Simply speaking, the book says:

Unfortunately, it increases the CPI by 1.1.

Where CPI is for clock cycles per instruction, if that matters. According to the choices the question provided, it actually means the increased value is 1.1 times of the original one (10% increase). It's the first time I have seen "by" meaning "to". Is it acceptable in daily English?

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The sentence really should have read:

Unfortunately, it increases the CPI by a factor of 1.1.

One would probably not find this sort of ambiguity in a math text, but it is certain that a factor of was implied.

Note, however, that

Unfortunately, it increases the CPI to 1.1

does not mean the same thing! This implies, the final value of the CPI, after the increase, is 1.1.

by is used to indicate a product, but usually in an explicit manner, e.g.

• Taxes increased by 10%.
• The new energy rating has decreased, by a factor of 1.5.

Indeed, in the absence of any context, I could be tempted to take

Unfortunately, it increases the CPI by 1.1

to mean 1.1 is added to the CPI, but I would really hard-pressed to do that! In a mathematical context, though, when one sees by, one should begin to think multiplication or division.

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+1 for the last sentence. In this particular context, I would understand "increased by" as a multiplication. In general, however, I would understand it as an addition. – b.roth Jan 13 '11 at 15:52
“but I would really hard-pressed to do that” – why? Doesn’t “increase x by y” mean exactly that? As in, “Christmas increased my weight by fifty pounds.” – Konrad Rudolph Jan 13 '11 at 17:05
@Konrad Rudolph: I included the hard-pressed part a few minutes after posting, just to counter some peer pressure :) After some thought, I now realize that, while in your excellent example, by implies an addition, it only emphatically does so when a unit is specified, e.g. increased...by 50 pounds/meters/watts, etc. A number on its own would be most likely read as a factor of multiplication. From my science background, I would battle hard to come to terms with, for instance, increases the CPI by 1.1. Units are very important! Ultimately, this ambiguity should have been avoided. – Jimi Oke Jan 13 '11 at 23:50
It make more sense to interpret the increase as the absolute numerical value in this case. It should be caused by the carelessness of the authors. It's also the first time I consider "increase by a factor of" seriously. I looked up in dictionary; the word factor has a meaning of "a quantity by which a given quantity is multiplied or divided in order to indicate a difference in measurement". – LLS Jan 14 '11 at 3:06
@Jimi: not only units: “five minutes later, the number of people in the room had increased by 10” – though I would use a completely different formulation (“… there were 10 more people in the room” or something like that), it’s nevertheless clear what is meant and as far as I know it’s correct – if unusual – English. – Konrad Rudolph Jan 14 '11 at 10:29

X increased by 1.1 → X is now 1.1 times the previous value of X (10% increase)

X increased to 1.1 → X is now 1.1 (before it was less than 1.1)

Note that this is my interpretation of increased by in this particular context. In general, however, I would interpret increased by as an addition, i.e. 1.1 added to the original value.

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Thanks for pointing out. – LLS Jan 14 '11 at 2:58

The use of "by" isn't indicating "to" in this case. It's indicating that the current CPI would be increased by another 10%, not to a maximum threshold of 1.1.

See Wikipedia's info on percentages. It may help explain further.

http://en.wikipedia.org/wiki/Percentage

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Agreed. If I see "to" separately, I will probably think the same thing. But it's not my point in this question. – LLS Jan 14 '11 at 2:58