Significant Figures in Addition/Subtraction Problems Explained

[meowers]

2340-100

For addition/subtraction problems you are supposed to use the number with the fewest digits to the right of the decimal point, but in this case, there are no decimals. My teacher gave an answer of 2200. Why is this the case instead of 2240 or 2000?

 

[cepheid]

You could write these values in scientific notation as 2.340e3 and 0.100e3. So, they both have the same number of decimal places, and their difference is 2.240e3 or 2240. So, following the rules that you've provided, that's the answer I would have given...

 

[CFede]

You can write it with decimal points like this 2340-100=(2,34-0,1)*1000

Then you perform the substraction, and the numer with the fewest numbers to the right of the decimal point is 0,1, so

(2,34-0,1)*1000=2,2*1000=2200.

The exact answer to the sibstraction would be 2,24, but since you are considering only one number to right of the decimal point, it gets approximated to 2,2.

 

[tiny-tim]

hi meowers!

divide by 1000, and you get 2.34 -0.1

then the number with the fewest digits to the right of the decimal point is 0.1

now convert back again … the rule tells you to use 100, and so to round 2240 to 2200

from the pf library …

Adding and subtracting:

Round-off the result to the highest decimal place to which any of the given numbers is rounded-off.

(If one or more given number is a whole number ending in zeros, then use the largest number of zeros in those given numbers; otherwise, use the smallest number of places after the decimal point; however also use common-sense, see below.)

For example, 571000 + 5300 = 576000, and 500000 + 5300 = 500000, but 571320 + 5300 = 576900, in each case using the largest number of zeros.

5.71 + 2351.2 = 2356.9, 5.7 + 2351.21 = 2356.9, 5.7 + 2351 = 2357, 5.7 + 2350 = 2360.​

 

[cepheid]

hi meowers!

divide by 1000, and you get 2.34 -0.1

then the number with the fewest digits to the right of the decimal point is 0.1

now convert back again … the rule tells you to use 100, and so to round 2240 to 2200

from the pf library …

Adding and subtracting:

Round-off the result to the highest decimal place to which any of the given numbers is rounded-off.

(If one or more given number is a whole number ending in zeros, then use the largest number of zeros in those given numbers; otherwise, use the smallest number of places after the decimal point; however also use common-sense, see below.)

For example, 571000 + 5300 = 576000, and 500000 + 5300 = 500000, but 571320 + 5300 = 576900, in each case using the largest number of zeros.

5.71 + 2351.2 = 2356.9, 5.7 + 2351.21 = 2356.9, 5.7 + 2351 = 2357, 5.7 + 2350 = 2360.​

Excluding the trailing zeros from either of the numbers given in the OP after dividing by 1000 makes no sense to me. All of those zeros are significant figures. Sig figs are relevant to measured quantities and the whole procedure exists to make sure that you accurately represent the certainty of the measurement. If somebody quotes me measurement as being 100 "units", then there are two things that had darn well better be true:

1. This person's measurement apparatus had better be precise to the nearest unit. If it's only precise to the nearest hundred units, he should write 1e2. He should not write something that can be interpreted as 1.00e2.

2. The person had better be certain, based on his measurement, that the true value lies between 99 and 101. In fact, he might even quote ± 0.5 as his uncertainty.

Am I wrong?

 

[CFede]

Excluding the trailing zeros from either of the numbers given in the OP after dividing by 1000 makes no sense to me. All of those zeros are significant figures. Sig figs are relevant to measured quantities and the whole procedure exists to make sure that you accurately represent the certainty of the measurement. If somebody quotes me measurement as being 100 "units", then there are two things that had darn well better be true:

1. This person's measurement apparatus had better be precise to the nearest unit. If it's only precise to the nearest hundred units, he should write 1e2. He should not write something that can be interpreted as 1.00e2.

2. The person had better be certain, based on his measurement, that the true value lies between 99 and 101. In fact, he might even quote ± 0.5 as his uncertainty.

Am I wrong?

I hadn't thought of it that way, but I think you are right. If a measurement is 100 units, it should be precise up to the unity. In that, sense its not the same to write 100 than 1e2, however, this is very sutile, I suppose that the idea on this problem is to treat 100 as 1e2.

But yeah, I think you're right.

 

[tiny-tim]

2340-100

If somebody quotes me measurement as being 100 "units", then there are two things that had darn well better be true:

1. This person's measurement apparatus had better be precise to the nearest unit. If it's only precise to the nearest hundred units, he should write 1e2. He should not write something that can be interpreted as 1.00e2.

2. The person had better be certain, based on his measurement, that the true value lies between 99 and 101. In fact, he might even quote ± 0.5 as his uncertainty.

Am I wrong?

meowers' teacher is obviously assuming that the 2340 is to 3 sig figs, and the 100 is to 1 sig fig, and in that case the answer of 2200 is correct

however, i'd normally be reluctant to believe that any measurement worth making was so inaccurate that it could only be made to 1 sig fig and that that fig was 1 !

that's a possible inaccuracy of 100% (if the "exact" measurement was 50.1)!

so i'd be inclined to say that 2340 minus 100 (or 2341 minus 100) was 2240

(but 2341 minus 500 is 1800)

in practice, the error would be given, or it would be obvious, eg if the question is "a bullet traveling at 2340 mph collides with a car traveling at 100 mph", and we know the 100 was estimated from skid marks, then it would probably be 100 rather than 90 or 110, but nobody would write that as 10e1

meowers, this issue (of how to write and read 100) is something you could raise with your teacher in the next class, as a discussion point! ​