How Many Paces Did It Take to Measure the Gym?

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SUMMARY

The discussion centers on calculating the number of paces taken to measure a gym with a length of 28 meters using a pace factor of 0.78 meters per pace. The calculation yields approximately 35.90 paces, which rounds to 36 paces when considering accuracy to the nearest quarter of a pace (0.195 meters). Participants clarify the significance of rounding and precision in measurements, emphasizing the importance of understanding significant figures in surveying. The conversation also touches on the historical context of the term "pace" in relation to measurement.

PREREQUISITES
  • Understanding of pace factor and its application in measurement
  • Basic knowledge of significant figures and rounding in mathematics
  • Familiarity with surveying concepts and measurement accuracy
  • Ability to perform unit conversions and calculations involving meters and paces
NEXT STEPS
  • Study the principles of significant figures in measurement
  • Learn about the use of pace factors in surveying and field measurements
  • Explore the historical context and evolution of measurement units
  • Practice solving measurement problems involving rounding and precision
USEFUL FOR

Students in surveying courses, educators teaching measurement concepts, and professionals involved in field measurements and accuracy assessments.

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Homework Statement


a person tries to measure the length of a gym by pacing across it with a pace factor of 0.78. How many paces accurate to 1/4 of a pace do you think did the student make?


Homework Equations





The Attempt at a Solution

 
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What is a 'pace factor'?
 
the 0.78 meters/ pace:)
 
Please show some attempt at this question so that others can see where you may be having difficulty. Have you included all the information given?
 
Doesn't it depend on the gymnasium length? What, 32.0 m? ggcflo, what is your gym length, in meters? If this problem is "really basic," as you stated in the title, why not answer it?
 
the length of the gym is 28. 1/4 of a pace is (0.78 x 0.25)=0.195.
how may paces accurate to 0.195m did the student make to get the length of the gym (28m).
28m x (1pace/0.78m) = 35.90 paces
the question I am having trouble with is how the part "accuarate to 0.195m"?

help and thanks again:)
ps: i thought the question was basic because it was on the first field exercise of my surveying 1 course..
 
welcome to pf!

hi ggcflo! welcome to pf! :wink:
ggcflo said:
a person tries to measure the length of a gym by pacing across it with a pace factor of 0.78. How many paces accurate to 1/4 of a pace do you think did the student make?
ggcflo said:
the length of the gym is 28. 1/4 of a pace is (0.78 x 0.25)=0.195.
how may paces accurate to 0.195m did the student make to get the length of the gym (28m).
28m x (1pace/0.78m) = 35.90 paces
the question I am having trouble with is how the part "accuarate to 0.195m"?

oh i see! :rolleyes:

(ggcflo, in future, please give us the full question at the start)

i think it just means the equivalent of sig figs or decimal places …

instead of a result like 476.3 being rounded to 476 or 480 or 500, it wants it rounded to the nearest 1/4 :smile:
 
Surveying instruments are usually graduated in degrees and minutes (sometimes fractions of a minute) and it is usually possible to take a reading, estimating to the nearest quarter of a division on the scale. That is presumably why you are being asked to solve this problem at an enlarged scale, using paces; so that you can visualise what eventually will be a very small error. So please make sure you understand it. Another way you could get into the question is: What is the smallest and largest number of paces required to measure the length of the gym, and can you do better than that?
 
I forgot to add that in Shakespeare's time, the petty pace was a unit of time instead of distance. :wink:


From http://www.enotes.com/shakespeare-quotes/tomorrow-tomorrow-tomorrow" …
To-morrow, and to-morrow, and to-morrow,
Creeps in this petty pace from day to day,
To the last syllable of recorded time​
 
Last edited by a moderator:
  • #10
ggcflo: Try this practice problem, and see what value and units you get for length x.

L = length = 25.45 m
pace_factor = 0.78 m/pace
precision = 0.25 pace
x = round[(L/pace_factor)/precision]*precision​

By the way, always leave a space between a numeric value and its following unit symbol. E.g., 0.195 m, not 0.195m. See the international standard for writing units[/color] (ISO 31-0[/color]).
 
  • #11
If the answer is 35.90 paces, then, to the nearest quarter, that is 36 paces, not 35.75 paces. Hence length = 36*0.78 m = 28.08m to the nearest quarter of a pace. Strictly, 28.08 + or - 0.5*0.195 But that gives an excessive claim to "accuracy". It needs rounding off. mmm...
 
Last edited:

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