Significant Digits Ruler -To what decimal point

[vvfrn3]

Significant Digits Ruler -To what decimal point
To what decimal point do I write the number 30 if the uncertainty is 0.0625?
The ruler has 1/8 marks.

Thank you :)

 

[berkeman]

Significant Digits Ruler -To what decimal point
To what decimal point do I write the number 30 if the uncertainty is 0.0625?
The ruler has 1/8 marks.

Thank you :)

Welcome to the PF.

You are required to show your Attempt at a Solution before we can offer any tutorial help. How would *you* approach this problem?

 

[vvfrn3]

I thought it would be 30.000 +- 0.0625 bc there are 3 sig figs in the uncertainty, but I'm not sure. :/
Also, should the uncertainty be rounded since it looks very precise? I'm so sonfused

 

[haruspex]

I thought it would be 30.000 +- 0.0625 bc there are 3 sig figs in the uncertainty, but I'm not sure. :/
Also, should the uncertainty be rounded since it looks very precise? I'm so confused

There are three sources of error here. One is that you are rounding to the nearest mark. That introduces an uncertainty of exactly ±0.0625. Next is any error in the placing of the marks on the ruler. You could handle that by rounding the first uncertainty up a little, ±0.064, say. Third is any error in your decision of which is the nearest mark. That's the same in nature as the second error, but statistically independent.
Now, suppose you decide the error is ±0.07 and you measured the value as 30.375. It would be quite appropriate to write the answer as, say, 30.375±0.070, strange though that may seem. But it would also be reasonable to compromise there, e.g. with 30.37±0.08.

 

[Nickie]

I would suggest writing the number 30 with two decimal points, as the uncertainty is 0.0625, which is equivalent to 1/16 on the ruler. This means that the number 30 falls between two marks on the ruler, specifically between the 30.00 and 30.06 marks. Including the second decimal point allows for a more accurate representation of the measurement within the given uncertainty.