Question

need help with conversions...
such as... Diamond (a form of elemental carbon) has a density of 3.513 g cm^-3. What is the density of diamond in pounds foot^-3?

Answer 1

First can you tell me what
1g is in pounds
and
1cm^3 is in in foot^3?

Answer 2

thats the problem i dont know the conversions or where to begin... i used to know them but that knowledge has disappeared

Answer 3

use wolfram alpha

Answer 4

I'm just lazy lol you can use google to but i will do all the work just one second

Answer 5

0.002205lb = 1g
3.531*10^-3foot^3 =1 cm^3

knowing this we set up the ratio

\[\frac{0.002205lb}{1g}(\frac{1cm^3}{3.531*10^{-3}foot^3}) = \frac{1*0.002205lb(cm^3)}{1*3.531*10^{-3}(g)foot^3}\]

Answer 6

now we multiply the density you have to convert it over the units you don't want will cancel out

Answer 7

\[\frac{1*0.002205lb(cm^3)}{1*3.531*10^{3}(g)foot^3} * \frac{3.513g}{1cm^{3}} = \frac{(1*0.002205lb(cm^3))*3.513g}{(1*3.531*10^{3}(g)foot^3)(1cm^{3})}\]

Answer 8

the conversion ratio should actually be

\[\frac{1*0.002205lb(cm^3)}{1*3.531*10^{3}(g)foot^3}\]

Answer 9

you just treat the units like numbers they cancel each other out

Answer 10

all exponents should be + I made a mistake by making them negative

Answer 11

you are left with
\[\frac{0.002205*3.513lb}{3.531*10^{3}foot^3}\]

Answer 12

do you follow?

Answer 13

i believe i am starting to... im trying to look through what you did and make something of it

Answer 14

just treat the units like numbers they divide to equal 1 so they don't effect the final answer

Answer 15

Just an aside when you see a negative exponent it just means that the number belongs in the denominator

The rule:

\[x^{-1} = \frac{1}{x}\]

Answer 16

\[x^{-2} = \frac{1}{x^2}\]
etc...

Answer 17

i know that about exponents but isn't density written as unit^-3

Answer 18

\[ 3.513g(1cm^{-3}) = \frac{3.513g}{1cm^{3}} = \frac{3.513g}{cm^{3}} \]

Answer 19

note you can divide any number by 1 and it wont change the numbers value

Answer 20

so that's where that's from...

Answer 21

yes negative units mean that the unit belongs in the denominator

Answer 22

so I simply set up a ratio to cancel the units

Answer 23

if you flip the ratios you can convert back to where you originally start btw

Answer 24

since we assume that we can always divide by 1 we just exclude it from the answer but it is there

Answer 25

do you follow?

Answer 26

The most important thing to do is look at the units like numbers. They will just cancel out like numbers

Answer 27

alright thank you

Answer 28

I think I made a mistake sorry I have a pretty bad migraine it is making mess up a lot all my senses are like super heightened it is really distracting

Answer 29

\[\frac{0.002205∗3.513lb}{3.531∗10^{-3}foot^3}\]

Answer 30

https://www.wolframalpha.com/input/?i=+3.513+g+cm^-3+to+pounds+foot^-3