formula for the % of increase between x & y?

Crux · 2009-10-19 08:17:13

Hey, I've started this chart out of curiosity, I thought it would be cool to see vs the standards I'm used to.
Basically I'm taking each step of gauge (of wire traditionally, but for this purpose piercing jewelery) in mm and converting the difference between each to a percentage. One's ears don't really stretch in millimeters, but in a percentage of increase between sizes, which is really why some steps are more difficult than others.

I originally thought I didn't need an algebra equation for this after looking at the first set of numbers..
1.2mm to 1.6mm (16g to 14g)
I figured there's a .4mm difference, so 1.2/.4=3, aka .4= 1/3 of 1.2, or 33.3%. So there's a 33.3% increase between 16g & 14g.
Checking this out to be sure my logic wasn't off, 1.6 does = 133.3..% of 1.2, as 1.2x1.33... = 1.6.

This all seemed to line up until I got to 2ga, which is measured sometimes as 6mm & sometimes 6.5mm.
4ga to 2ga being 5mm to 6mm: 1mm difference, 1=1/5 of 5, or 20%. this checks out
4ga to 2ga being 5mm to 6.5mm: 1.5mm difference, 5/1.5=3.33..., 3.3.. as a fraction is 1/3, so 1.5 = 1/3 of 5? This makes no sense.
I think I'm making some sort of juvenile error here as it's been a minute since my last math class, but 1.5x3 is definitely 4.5.
1.5x3.33.. is 4.99.. , but if 3.33.. = 1/3 thennn.. idk I think I've trapped myself in my own false positive, haha.
Anyway, my real problem was one step further, as I'd overlooked this until just now as 5 to 6=20% / 5 to 6.5 = 33.3% made sense to me.

2ga to 0ga being 6mm to 8mm: 2mm difference, 6/2=3, aka 2 = 1/3 of 6, so 33.3% increase
2ga to 0ga being 6.5mm to 8mm: 1.5mm difference, 6.5/1.5=4.33...?
How is a 1.5mm difference a LARGER percentage of increase than a 2mm difference? Even if 1.5 were a larger % of 6.5 than 2 was of 6 (which it's not, a smaller number is in no way a larger percentage of a larger number than a larger number is of a smaller number, if you follow.. haha) that still doesn't mean it's a bigger jump, as they're both jumping to the same number.

I think I've just confused myself all up here. A smaller number will go into a bigger number more times, obviously, but then doesn't that mean my logic here is totally flawed? All of my percentages would be off then because the smaller the difference the larger (more) times it would go into the original number, and I've been turning that number into my % of increase this whole time...

Anyway, I was having fun playing with math and math theory again, and after asking my girlfriend and mum about my logic issue to no avail I thought I'd come here, as I'd still like to complete this chart.

bobbym · 2009-10-19 16:34:08

Hi;

4ga to 2ga being 5mm to 6.5mm: 1.5mm difference, 5/1.5=3.33..., 3.3.. as a fraction is 1/3, so 1.5 = 1/3 of 5? This makes no sense.

This is as far as I have gotten in your thinking so I don't know if there is an error later on but:

3.33... as a fraction is not 1/3. 1.5 = 1/3.333... of 5.

Last edited by bobbym (2009-10-19 16:35:31)

Crux · 2009-10-20 07:04:39

3.33... as a fraction is not 1/3.

it's not? I learned throughout middle junior and high school that 3.33... as a fraction would be 1/3 & vice-versa. Makes sense, 3.3333333, 6.6666666, 9.999999... 33% 66% 99%, any base 10 ÷ 3 = 3.33... / 33.3... / 333.333... / etc.

1.5 = 1/3.333... of 5.

right, i realized this around where I said

1.5x3.33.. is 4.99..

Whatever semantic I may have gotten caught up on back there, I guess my real question is just how would I go about finding the % of change between x and y? Isn't there already a nice formula written for that? It just seems like something that would come up so frequently I feel like some great old mathematician has to have already written one.

Fruityloop · 2009-10-20 11:27:36

Hi Crux,
I'm not totally sure where your confusion is but it seems as though you're taking the reciprocal of the percentage change and trying to make sense of it. Always remember that to find the percentage change take the difference between the two amounts and divide by the original amount.

6/2 = 3 so we need the recriprocal for the percentage change (1/3) = 0.3333.....
So we have 6.5/1.5 = 4.3333.....
now to find the percentage change we need the reciprocal (1/4.3333....) = 23.08%

I hope this helps,
Fruityloop

Crux · 2009-10-20 16:32:02

So.. just put a 1 over it & convert that decimal to a percentage?
That's easy. Thanks.

bobbym · 2009-10-20 16:51:56

it's not? I learned throughout middle junior and high school that 3.33... as a fraction would be 1/3 & vice-versa. Makes sense, 3.3333333, 6.6666666, 9.999999... 33% 66% 99%, any base 10 ÷ 3 = 3.33... / 33.3... / 333.333... / etc.

3.333... is not 1/3 , .33333.... is 1/3. 3.3333 is 10/3

If I asked you for 1/3 of a dollar would you give me $ 3.33 or would you give me 33 cents?

Last edited by bobbym (2009-10-20 16:54:46)

Crux · 2009-10-21 09:01:22

sorry, that's what I meant. that point three repeating is one third.
Not trying to be elitist here, was just wondering the formula for % of change, could care less about point three repeating issues, really.

bobbym · 2009-10-22 07:16:12

Hi Crux;

I understand your feelings but I can't say that I agree with them.

Math Is Fun Forum

#1 2009-10-19 08:17:13

formula for the % of increase between x & y?

#2 2009-10-19 16:34:08

Re: formula for the % of increase between x & y?

#3 2009-10-20 07:04:39

Re: formula for the % of increase between x & y?

#4 2009-10-20 11:27:36

Re: formula for the % of increase between x & y?

#5 2009-10-20 16:32:02

Re: formula for the % of increase between x & y?

#6 2009-10-20 16:51:56

Re: formula for the % of increase between x & y?

#7 2009-10-21 09:01:22

Re: formula for the % of increase between x & y?

#8 2009-10-22 07:16:12

Re: formula for the % of increase between x & y?

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