Question

A particular brand of gasoline has a density of 0.737
g/mL
at 25

∘
C
. How many grams of this gasoline would fill a 15.7
gal
tank (
1US gal=3.78L
)?

Answer 1

I got 43.7 g

Answer 2

@Vocaloid

Answer 3

hm, I don't think so, you might have inverted a conversion factor somewhere.

anyway so we start w/ the density

0.737g/mL

to convert from mL to L we will actually multiply by 1000 (this seems counter-intuitive but since mL is in the denominator and we want L to also be in the denominator, we perform this conversion factor.

Answer 4

now, since we want L to gallons, we multiply again by the conversion factor 3.78L/1 gallon

Answer 5

3.78

Answer 6

cancelling our units gives us a g/gallon rate

after which, since we have 15.7 gallons we just multiply the end result by 15.7

Answer 7

2785.86

Answer 8

so in the end we have 0.737g * 1000 * 3.78 * 15.7

Answer 9

43738.002

Answer 10

yeah I think that's right just lemme double check my solution

Answer 11

anyway, yeah, that should be right,

since they only give us three sig figs we should round 43738.002 to 43700g

Answer 12

A block of metal has a width of 3.2
cm
, a length of 17.1
cm
, and height of 3.8
cm
. Its mass is 1.4
kg
. Calculate the density of the metal.


Okay so I calculated the l*w*h and got 207.936 and i also know that there are 1000cm in a kilogram

Answer 13

What is the next step. I am having trouble with conversions

Answer 14

(be careful about that 1000cm = 1 kg logic, those aren't measuring the same thing so you can't really compare them)

anyway, density = mass/volume so 1.4 kg/207.936 cm^3 then just simplify to get your density

Answer 15

okay so the l times w times h that I calculated in the volume as a whole?

Answer 16

yes, so the L*W*H gives you 207.936 cm^3 as the volume

then your mass is 1.4kg

so the density is just mass/volume

Answer 17

but the units are different, don't I have to convert it or leave as is

Answer 18

the units of density are mass/volume, so in this case kg/cm^3 would be your end units

Answer 19

(unless the question specifies something different)

Answer 20

oh right. its two different units in the formula anyways..

Answer 21

I got .0069732

Answer 22

but to two sig figs it would be .01?

Answer 23

.01 m^3

Answer 24

.01 kg/cm^3

Answer 25

hm, not quite, you rounded up a bit too much

.0069732

starting from the left we just round up the 6 to a 7 since we have a 9 after it

then it becomes 0.0070

Answer 26

oh right cause the two zeroes would be insignificant?

Answer 27

yes, leading zeros after a decimal are insignificant

Answer 28

the 0 at the end is significant

Answer 29

okay so final answer as 0.0070

Answer 30

0.0070 kg/cm^3 yup

Answer 31

A 10-g sample of aluminum has a volume of 3.70 cm3. What is the density of aluminum?

Answer 32

density = 10g/3.70cm^3 = 2.70 g/cm^3

Answer 33

how many sig figures on that 10? is it 10.0 or 10. or 10?

Answer 34

2?

Answer 35

your calculation is correct, im just wondering about the sig figs

Answer 36

it just says 10-g

Answer 37

\(\color{#0cbb34}{\text{Originally Posted by}}\) @zarkam21
A 10-g sample of aluminum has a volume of 3.70 cm3. What is the density of aluminum?
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 38

is it a multiple choice or free response?

Answer 39

because "10" actually only has 1 sig fig :S

Answer 40

multiply choice

2.70 g/cm^3
3.70 g/cm^3
0.370 g/cm^3
3.70 x 10^1 g/cm^3

Answer 41

I just did it as is, the way we just did the previous problem

Answer 42

oh yeah in that case it's 2.70