# Homework Help: Significant Digits Ruler -To what decimal point

1. Apr 23, 2013

### 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 :)

2. Apr 23, 2013

### Staff: Mentor

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?

3. Apr 23, 2013

### 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

4. Apr 23, 2013

### haruspex

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.