Question

.-.

Answer 1

you can only keep 3 significant figures, since that's the most you have in any of the input values.

So 40.7 cm^3 should be correct.

Answer 2

ok thanks :) i got confused on this because they all have 2 digits after the decimal, so i figured the answer might have 2 digits after it too :/

Answer 3

actually, you are more correct than me... doesn't change the answer, but you are correct to count significant figures AFTER the decimal, not including the number before the decimal.

Otherwise, 12345.6 would be as significant as 0.123456, which is not true.

Answer 4

wait, but both of those numbers have 6 sig figs?

Answer 5

so their product would also have 6 sig figs too?

Answer 6

or what :l

Answer 7

no, the first one only has 1 sig-fig... the other has 6, so the product would only have 1 sig fig after the decimal.

Answer 8

The idea is that you can't "add information" (i.e. precision) when you multiply numbers... if one number is only precise to one significant figure after the decimal, then that is the level of precision in your final answer even if the other number is expressed with 5 or 6 significant figures.

Answer 9

so the answer would be 1524.1? not 1524.14?

Answer 10

Augmented knowledge via internet:
http://www.usca.edu/chemistry/genchem/sigfig2.htm

Answer 11

yes, in my example, you take the whole number part as-is... so 1524... and then round off the decimal part to make it have one significant figure, corresponding to the LEAST number of sig fig's in the original numbers (12345.6 has one sig fig).

Answer 12

So it's 1524.1383936 but it must be rounded to 1524.1

Answer 13

but i think you only do that with addition and subtraction

Answer 14

Hm. I should have read more first and waited to start talking :)

We're both part right...

Answer 15

For adding and subtracting, you count the digits after the decimal, and the sum/difference can have no more than the least of the inputs.

For multiplying and dividing, it looks like you count ALL significant digits, even those to the left of the decimal. Then your answer must be rounded to have no more than the least.

Answer 16

but, for that product, 12345.6 and 0.123456 both have 6 sig figs.. so the product should be 1524.1383936 rounded to 1524.14.

Answer 17

ok, thanks again for the help :)

Answer 18

Glad to help... I just wish I'd reviewed what I thought I knew before I opened my mouth on this one :) embarrassing!

Answer 19

lol that's ok, i do it all the time

Answer 20

can you help me with another thing?

Answer 21

the densities i recorded for part 2 are: 8.7g/mL, 8.5g/mL, and 8.2g/mL
and the densities i recorded for part 3 are: 0.626g/cm^3, 0.446g/cm^3, and 0.774g/cm^3

would you consider the densities for part 2 precise? and part 3?

Answer 22

this is what i wrote, but idk if it's right

In part II, the range of densities is 0.5g/mL. In part III, the range of densities is 0.328g/cm3. To me, both parts have good precision in their densities.

Answer 23

Are those measurements three measurements of the same thing? Or three different things?

Precision is a way to describe how tightly a group of measurements of the same quantity are found. If you measure density 3 times and get very similar results, your measurements are precise. They may all be wildly wrong due to equipment problems, but you at least have a precise method of measuring, since it produces mostly similar measurements.

Answer 24

But a question of "is such and such precise" is a terrible question :(

Precise compared to what??

Answer 25

yea, part 2 are the densities of the same rock, and part 3 are the densities of the same block of wood

Answer 26

Those densities are precise to some extent, but it depends on how precise the measurements need to be (but I know you don't have much more to work with here...)

Measurement with a ruler can be reasonably precise, but if you are building mirrors for the Hubble telescope, a ruler's measurement is no where near precise enough.

Anyway, your response was probably fine, especially since it's a subjective question and you showed some understanding of the concept when you explained the range of values you observed.

Answer 27

well, this is the actual question: In parts II and III of the lab you used different sized objects in each trial. Compare the density values that you calculated for these items, how do the three trials compare?

but i figured they would want me to answer using accuracy and precision since that's what i learned during the lesson. and since i don't know the accepted densities, i can't say they're accurate

Answer 28

would my answer be sufficient?

Answer 29

You can conclude that your density values have reasonable precision and mention the range of the values, and you can say what you just said about accuracy... you can compare the three trials but you don't know the "accepted" density so you don't know if your measurements are accurate.

I think you're on the right track. I think your answer is sufficient :)

Answer 30

mmk, thanks :)