Can you divide different mass units without unit conversion?

[sideshowcris]

I've got a problem that I'm starting to second-guess myself on. I've got a huge number expressed in lbs (too huge for a calculator) that I need to divide by a smaller number in lbs. The person who's asked me to calculate this number suggested I convert the huge number to tons so it can be calculated automatically in an Excel spreadsheet, but I seem to recall being taught that the units of measurement have to match in a case like this. I'm almost certain I'm correct, because when I divided the tons number by the small lbs number I got a different number than when I divided the bigger lbs number in longhand (obviously). I went to Google looking to see if I was doing something wrong and I only found more vagaries (examples about multiplying speed and time, etc.) so I'm well and truly stumped. Someone please tell me whether I'm right or the other person is right.

 

[Dr.Peterson]

I've got a problem that I'm starting to second-guess myself on. I've got a huge number expressed in lbs (too huge for a calculator) that I need to divide by a smaller number in lbs. The person who's asked me to calculate this number suggested I convert the huge number to tons so it can be calculated automatically in an Excel spreadsheet, but I seem to recall being taught that the units of measurement have to match in a case like this. I'm almost certain I'm correct, because when I divided the tons number by the small lbs number I got a different number than when I divided the bigger lbs number in longhand (obviously). I went to Google looking to see if I was doing something wrong and I only found more vagaries (examples about multiplying speed and time, etc.) so I'm well and truly stumped. Someone please tell me whether I'm right or the other person is right.

First, what is the number? Excel (and many calculators) can handle very large numbers.

Second, why do you want to divide the two weights, and what will you do with the result?

You may need to give the details about what you are doing so we can be sure it makes sense. Context can be important.

 

[sideshowcris]

So the huge number is pounds of carbon dioxide, and the goal is to express that in an equivalent number of plastic bottles given these conditions:

1 lb plastic bottles = 4.7 lbs carbon dioxide
1 lb plastic bottles = 36 individual plastic bottles

90,283,846,958 lbs carbon dioxide = X individual plastic bottles
Solve for x

It seems to me like the equation should be 90,283,846,958/4.7*36 = x, but when I plug all that into Excel, it brings back a ########### error. The suggestion was to convert 90,283,846,958 into tons (90,283,846,958/2000 = 45,141,923) and then do the equation again with tons/lbs (45,141,923/4.7*36 = x), but that obviously gets me a wildly different number when I do the first equation by longhand vs the second equation in Excel. So is my logic breaking down here due to my lack of math understanding?

 

[lex]

I suspect your Excel error is not an error but just that you need to widen the column to see the answer.

Double click the line between the letters 'A' and 'B'.

 

[JeffM]

There are at least four ways to solve this problem.

(1) The error indicated by ### indicates that the number cannot be DISPLAYED in a cell of the given size. You can expand the size of the cell to eliminate the error. Do you know how to do that?

(2) You can change the format of the cell to "Scientific" and leave the size of the cell alone.

(3) You could convert everything to tons

[MATH]90,283,846,958 / 2000 = 45,141,923.479 \text { tons of carbon dioxide}[/MATH]
[MATH]4.7 \text { pounds of CO_2 per pound of bottles} = 4.7 \text { tons of CO_2 per ton of bottles}[/MATH]
[MATH]36 * 2000 = 72000 \text { bottles per ton of bottles}[/MATH]
[MATH](45,141,923.479) \div 4.7) * 72000 = 691,535,849,040[/MATH]
Which is exactly the same answer that you get from

[MATH](90,283,846,958 \div 4.7) * 36 = 691,535,849,040[/MATH]
I do not advise changing units because, unless you are comfortable with dimensional analysis, it is very easy to make a blunder.

(4) Recognize that all of these numbers are estimates and exactitude is ridiculous. Do you really believe that every plastic bottle has identical carbon content and it just happens that the carbon dioxide released by exactly 36 of those uniform bottles is exactly 4.7 pounds. So make your life easy and say you have approximately 90.3 BILLION pounds and

[MATH](90.3 \div 4.7) * 36 \approx 691 \text { billion bottles.}[/MATH]
You can do that on the cheapest of hand calculators.

 

[sideshowcris]

(4) Recognize that all of these numbers are estimates and exactitude is ridiculous. Do you really believe that every plastic bottle has identical carbon content and it just happens that the carbon dioxide released by exactly 36 of those uniform bottles is exactly 4.7 pounds. So make your life easy and say you have approximately 90.3 BILLION pounds and

That's essentially what I'm doing, but I'm just trying to make sure I have the proper approximate calculation. When I did it the way my colleague suggested, I got 341 million bottles, which is a far cry from 691 billion.

 

[lex]

Yes, you would have to multiply that answer by 2000 again at the end to get the correct number of bottles.
The excel solution is probably the easiest.
However, if you were doing it all manually on a calculator, you are probably best 'changing the units' of the number i.e. if you want to do 90,283,846,958/4.7*36 then type the large number in as a number of billions:
90.283846958/4.7*36 and your answer (rounded by the calculator) will be in billions (of bottles)

 

[lookagain]

.
.
[MATH](90,283,846,958 \div 4.7) * 36 = 691,535,849,040[/MATH].
.
. . . that the carbon dioxide released by exactly 36 of those uniform bottles is exactly 4.7 pounds.
So make your life easy and say you have approximately 90.3 BILLION pounds and

[MATH](90.3 \div 4.7) * 36 \approx 691 \text { billion bottles.}[/MATH]

\(\displaystyle (90.3 \div 4.7)*36 \ = \ 691.6... \ \approx \ 692 \ \text { (billion bottles).} \)

The rounded whole number of billion bottles agrees with what would be the corresponding
rounded value when applied to the value at the top of this quote box.

 

[JayJay]

It may be worth noting that the lb/ton conversion factor used, 2,000, is incorrect. 1 ton = 2,240 lb.

 

[lex]

It may be worth noting that the lb/ton conversion factor used, 2,000, is incorrect. 1 ton = 2,240 lb.

I think there may be a difference between a British ton and a North American ton.

 

[JayJay]

Yes, I am so used to UK units I forgot the US ton is different.