This is the question and the answers are below each one: Notice that all of thes

Question

This is the question and the answers are below each one:

Notice that all of these answers are from the solutionmanual.

A box has a length of 18.1 cm and a width of 19.2 cm, and it is20.3 cm tall.

a. What is its volume?

b. How precise is the measure of length? Of volume?

Answer: nearest tenth of a cm; nearest

c. How tall is a stack of 12 of these boxes?

Answer: 243.6 cm

Now for (a) what are the steps that I have to follow in order toget an answer like the stated one (i.e. do I round the resultingvolume number first then convert to scientific notation taking intoconsideration the number of scientific digits that I have to haveor what?How?) the resulting volume is 7054.656 if i round itup first, I would get 7055 then convert to scientific notation Iget 7.06 * 10^3 which is different to the answer stated, pleasehelp?

Also for (b), when it says how precise, Does it mean ±half the smallest division on the scale or to the nearest decimalplace?

What does it mean by (nearest 10 cm3) for the volumeprecision?

And for (c) doesn't the answer has to be to three significantdigits (i.e. 20.3 * 12 should equal 244) since 20.3 has threesignificant digits?? (and isn't 12 is not considered for how manysignificant digit it has since it is a counting number??? so wedon't have to take it into consideration?? right)

Thank you

Explanation / Answer

I just multiplied the 3 numbers as given to get7054.656cm3. Since the value with the least number ofdigits has 3 digits, I have to assume I only have 3significant figures so the answer looks like 7050m3 or7.05x105cm3 In both the case of 1/10th a cm and 10cm3 you'relooking at the third digit of the number. You're absolutely rightabout the plus and minus but we only really use those in the lab.Normally if you have a number like 12.34+.04cm, you're safecalling it 12.3cm. What it means by 10cm3 is that sinceyou have precision to the highest 3 digits, the lowest of these hasa value in the range of 10cm3 and thus that is yourprecision. For the third problem, we're not combining measurements, we'rejust counting the ones we have 12 times. Since we didn't change thedimensions, we're still precise to the tenth of a cm.

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