How Should Time and Distance Uncertainties Affect Calculations in Physics Labs?

In summary: This would give you 0.17 ±0.03 h and 2.83 ±0.03 h, I think.In summary, the lab question involves recording the time and distance of a car traveling from Point A to Point B. The odometer gave a distance within 100 m, resulting in an estimated uncertainty of ±0.1 km for d. The time was recorded at equal intervals of 10 minutes, with an estimated timing error of ±0.2 minutes. This translates to a timing error of ±3.3E-3 hours for Δth. It is suggested that the median value and error range should be presented with the same number of decimal places. Therefore, the median values of 10.0 minutes and
  • #1
John_tawil
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Homework Statement


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
KCJfOZO.png


Homework Equations


1min = 1/60 hrs

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
 
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  • #2
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
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
John_tawil said:
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?
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.
 
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What are significant figures and why are they important?

Significant figures are digits in a number that represent the precision of a measurement. They are important because they help communicate the level of accuracy and precision in a measurement, which is crucial in scientific calculations and data analysis.

How do I determine the number of significant figures in a given number?

The rules for determining significant figures can vary slightly, but generally, any non-zero digit is significant, zeros between non-zero digits are significant, and zeros at the end of a number after a decimal point are significant. Zeros at the beginning of a number before a decimal point are not significant. Additionally, numbers written in scientific notation are considered to have all digits significant.

What are the rules for rounding when dealing with significant figures?

When rounding a number to a certain number of significant figures, the general rule is to round to the last significant digit. If the digit to the right of the last significant digit is 5 or higher, round up. If the digit is 4 or lower, round down. If the digit to the right of the last significant digit is 5 and there are no other non-zero digits after it, round to the nearest even number.

How do significant figures affect mathematical operations?

In mathematical operations, the result should be rounded to the same number of significant figures as the factor with the fewest significant figures. For addition and subtraction, the result should have the same number of decimal places as the factor with the fewest decimal places. For multiplication and division, the result should have the same number of significant figures as the factor with the fewest significant figures.

How do I use significant figures in scientific notation?

When using scientific notation, the coefficient should have the same number of significant figures as the original number, and the exponent should indicate the number of decimal places in the original number. When multiplying or dividing numbers in scientific notation, the coefficients should be multiplied or divided and the exponents should be added or subtracted. When adding or subtracting numbers in scientific notation, the exponents should be the same and the coefficients should be added or subtracted.

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