Relative Percentage vs Percentage Change

Question

If I have a number say "500" and I say that it spiked 4 times (400%) of the original value i.e. "2,000". Does that make sense mathematically and grammatically because I'm talking about relative percentage? Or is that a term in my mind at the minute.

I've been searching on this for a while now and have a feeling that there's two different terms to use when I was to say "increase by 300%" or "400% spike of the original value".

Any thoughts?

Answer 1

This is more of English language issue than math issue. Let $v$ denote the original value.

• To say that something "increased by x% of original value" means the new value is $v+\dfrac{x}{100}v$.
• To say that something "spiked to x% of original value" means the new value is $\dfrac{x}{100}v$.

I emphasized the prepositions, because they are what makes the difference here: "by" refers to the amount of change, "to" refers to the new state of things.