# The answer of a 2 sig calculation 0,098 = 0,10 ?

1. Apr 26, 2010

### QED-Kasper

the answer of a "2 sig" calculation 0,098 = 0,10 ?

I did some university entry examination questions. There were values of some properties like mass, gravity etc given, they all had 2 significant figures. After using them in my calculations for some problem, I got the following answer on my calculator: 0.098. So sticking to the rule of giving your answer to the same sig. figures as the measurement with the least sig. figures I left that as my answer. However the answer on the solution sheet was rounded to 0.10, which also has 2 sig figures.

Both answers having the same amount of sig figures, which one is correct and why? Thanks :)

Last edited: Apr 26, 2010
2. Apr 26, 2010

### mgb_phys

Re: the answer of a "2 sig" calculation 0,098 = 0,10 ?

0.098 is 2 sig figures, 9.8E-2

3. Apr 26, 2010

### QED-Kasper

Re: the answer of a "2 sig" calculation 0,098 = 0,10 ?

You must have raced trough my post very fast, haha. I know what significant figures are without any problem. The problem is that the solution sheet gives the answer to some question as 0,10. But I left my answer as 0,098. Which is what i got on my calculator after doing the calculation (involving only multiplication and division) for the problem. I did that because this answer has two significant figures so it complies with the "sig. fig. rule".

So the problem is that both answers have two sig. figs., but one has been rounded from 0,098 (which is the answer on the calculator) to 0,10 and the other is the answer calculated without rounding. I was wondering why the book gives the answer as 0.10 if 0,098 has two significant figures already and needs no rounding.

4. Apr 26, 2010

### mgb_phys

Re: the answer of a "2 sig" calculation 0,098 = 0,10 ?

You could argue that if you have a lot of steps with only 2sf then your answer loses 1% accuracy at each stop so quoting 2sf when the answer is so close to 0.1 is a bit optimistic.
But in that case the answer should be 0.1

Exams answers aren;t always correct - TAs are human too.

5. Apr 26, 2010

### diazona

Re: the answer of a "2 sig" calculation 0,098 = 0,10 ?

I'd be inclined to agree with you that 0.098 is correct, or at least better, since it's more informative. Both answers do follow the "rule" of keeping the fewest significant figures in a product.

To be honest, the whole significant figure system is just a time-saving approximation for error propagation. In a real experiment you'd probably quote your answer plus-or-minus some calculated uncertainty, and the uncertainty would tell you how many digits are meaningful.

6. Apr 27, 2010

### QED-Kasper

Re: the answer of a "2 sig" calculation 0,098 = 0,10 ?

Ok guys, that should do. Thank you for helping me :)

7. Apr 27, 2010

Staff Emeritus
Re: the answer of a "2 sig" calculation 0,098 = 0,10 ?

Which is a very good point: 0.10 means "between 0.095 and 0.105", i.e. you know it to +/- 5%. 0.98 means "between 0.975 and 0.985", or +/- 0.5%. This could be important.

8. Apr 28, 2010

### QED-Kasper

Re: the answer of a "2 sig" calculation 0,098 = 0,10 ?

So what is the convention in these type of situations? Do you leave it to be 0.098 (i.e. +/- 0,0005) as was the exact result on the calculator (with all values used in the calculation having two significant figures), or do you round up to 0.10 (i.e. +/- 0,005)?
Both answers are correct to two significant figures. It's a special situation because the result on the calculator is so close to the number 10.

9. Apr 28, 2010

### mikeph

Re: the answer of a "2 sig" calculation 0,098 = 0,10 ?

Question is, why are you even touching a number which is already in 2 s.f. format?

write the answer as 9.8e-2; then rounding to 10e-2 is actually making it one significant figure.

Last edited: Apr 28, 2010