How Many Paces Did It Take to Measure the Gym?

• ggcflo
In summary, the student tried to measure the length of a gym by pacing across it with a pace factor of 0.78. The attempt at a solution is to use paces to measure the length and round off the result to the nearest quarter of a pace.
ggcflo

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?

The Attempt at a Solution

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!
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!

(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

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.

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​

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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 (ISO 31-0).

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...

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What is surveying and why is it important?

Surveying is the process of measuring and mapping the land and other features of the earth's surface. It is important because it provides accurate information for planning and construction projects, as well as for land ownership and legal purposes.

What are the different methods of surveying?

The two main methods of surveying are field surveying, which involves physically measuring and mapping the land, and remote sensing, which uses technology such as satellites and aerial photography to gather data.

What equipment is needed for surveying?

The specific equipment needed for surveying depends on the method being used, but some common tools include a theodolite, total station, GPS receiver, and surveying rods. Other equipment may also include measuring tapes, levels, and markers.

What are some common challenges in surveying?

Some common challenges in surveying include difficult terrain, weather conditions, and obstacles such as buildings or trees. Technical challenges may also arise, such as maintaining accuracy and resolving conflicting data.

What are some applications of surveying?

Surveying has a wide range of applications, including civil engineering projects such as road construction, building construction, land development, and environmental projects. It is also used in mapping and measuring natural resources, conducting land surveys for legal purposes, and creating geographic information systems (GIS).

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