# Significant figures Help

1. Apr 23, 2015

### John_tawil

1. The problem statement, all variables and given/known data
This is a lab question. I'll summarize with key information.

Car traveling from Point A to Point B. You record the time and distance.

"Since the odometer gave the distance within 100 m, you estimated the uncertainty in d to be (Δd = ±0.1 km). Regarding the time, even though you did your best to take the meter reading at equal time intervals of 10 minutes, you still estimated a timing error of about 12 seconds (or Δtm = ±0.2 min)."

Here is the table they give you and we have to fill in the time in hours

2. Relevant equations
1min = 1/60 hrs

3. The attempt at a solution
At first, I look at the 12 seconds as 2 sig figs so my Δth should also be 2 sig figs... thus Δth = ±3.3E-3 hrs

I'm confused about the data they've given. 10.0 is 3 sig figs and 170.0 is 4 sig figs. So would my
10.0 ± 0.2 min become 1.67E-1 ± 3.3E-3 hrs
170.0 ±0.2 min become 2.833 ± 3.3E-3 hrs

2. Apr 23, 2015

### haruspex

Since you are quoting error ranges for the data, it is not a sin to have more digits than can strictly be justified. (It matters more when error ranges are not stated because in that case the reader infers the error range from the significant digits shown.)
But I do think it is wrong to have the error margin and the median terminating at different decimal positions. If you are going to quote the error range down to thousandths of an hour then you should do the same for median values.

3. Apr 23, 2015

### John_tawil

The lab deals with uncertainty and significant figures so I can't have more than I need because I'll lose points. Based on the information given, what do you guys think should my 10.0 min and 170.0 min be converted to?

4. Apr 23, 2015

### haruspex

Then I fear you are dealing with the opinions of your teacher more than with any real logic. I can't comment further without knowing exactly what you have been taught.
However, I do stand by my second observation, that the last digit should be at the same decimal place in median and error.
Edit: one more thought... arguably, you should always round the error range up, so 1/3 becomes 0.34, say, not 0.33.