How Do You Apply Sig Figs in Calculations and Trigonometry?

[jaydnul]

Actually multiple questions:
(1) Am i supposed to use the rules of sig figs all the way through a calculation or just for the final answer? If not, how do i know when the proper time to use them is? The reason i ask is because if you have, say, 2/3, the answer is .666666 repeating, but according to the rules of sig figs, its .7, but this isn't as accurate.
(2) When using trig functions, do I use the amount of least sig figs or least decimal places? I would assume sig figs since a trig function is just division.

Thanks

 

[collinsmark]

Actually multiple questions:
(1) Am i supposed to use the rules of sig figs all the way through a calculation or just for the final answer? If not, how do i know when the proper time to use them is? The reason i ask is because if you have, say, 2/3, the answer is .666666 repeating, but according to the rules of sig figs, its .7, but this isn't as accurate.
(2) When using trig functions, do I use the amount of least sig figs or least decimal places? I would assume sig figs since a trig function is just division.

Thanks

The quick answer is you should use more significant figures when working out the intermediate steps in the calculation, then apply your significant figure rule at the very end.

But here a couple of additional points.

• The significant figure rules are between you and your instructor (e.g., three significant figures, four significant figures, etc). There are not any universal rules regarding this. In the future, you might end up with different significant figure rules. Whatever the case, my advice still applies: use more significant figures in the intermediate steps, and apply the significant figure rules only at the very end.
• Your example of 2/3 (.666666 repeating) being .7 is only one significant figure (I'm betting your instructor's rules are more than that). The number of significant figures starts after ignoring all leading zeros. So if your rule is three significant figures, 2/3 comes to 0.667. For four significant figures it comes out as 0.6667.

 

[Borek]

The quick answer is you should use more significant figures when working out the intermediate steps in the calculation

I believe these are technically called guard digits.

Whatever the name is, only the final result gets rounded (unless one wants to report intermediate results - then they should be reported rounded, but not used rounded for calculations).

The significant figure rules are between you and your instructor (e.g., three significant figures, four significant figures, etc). There are not any universal rules regarding this.

Not exactly - there are more or less universal rules about how to determine number of significant digits in the final result, based on the significant digits in the data.

The reason i ask is because if you have, say, 2/3, the answer is .666666 repeating, but according to the rules of sig figs, its .7, but this isn't as accurate.

Depending on the context 2/3 can be an exact value, with infinite number of significant digits. You don't round kinetic energy to 1 significant digit just because 2 in \frac {mv^2}{2} is written with one significant digit.

Don't worry too much about sigfigs. There are much better ways of dealing with uncertainties. Sigfigs are just an approximate rule of thumb.

 

[HallsofIvy]

"Significant figures" are important in giving honest answers. If you measure the distance traveled as 58.67 km in 1.3 hours then you have measured distance to 4 significant figures while time is measured only to 2 significant figures. That means that the distance could be anywhere from 58.665 to 58.675 km and the time could be any where from 1.25 hours to 1.35 hours.

Just dividing 58.67 by 1.3 would give 45.130769230769230769230769230769... "km per hr". A calculation cannot be more accurate than the least accurate measurement so the correct statement would be that the speed was 45 km/hr- it could be any where from 44.5 to 45.5 km/hr. To say any more would imply a more accurate measurement. Writing the speed as 45.1 km/hr would imply that we are sure the speed is between 45.05 and 45.15.