Converting 100 Yards to Centimeters: Dimensional Analysis Explained

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Discussion Overview

The discussion revolves around the conversion of 100 yards to centimeters using dimensional analysis, with a focus on the proper handling of units in calculations. Participants explore various methods and express confusion regarding unit assignments and the interpretation of results.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant attempts to set up the conversion but struggles with the method, indicating a lack of clarity on dimensional analysis.
  • Another participant emphasizes the importance of showing work and understanding the conversion process.
  • Multiple participants provide the conversion calculation, stating that 100 yards equals 9144 cm, followed by dividing this by the length of a paperclip to find a numerical value.
  • Concerns are raised about the proper assignment of units, with participants questioning how to express the final result correctly.
  • Some participants argue that the calculations presented do not clearly show the conversion to paperclips, leading to confusion about the final answer.
  • A later reply insists on the necessity of including units in calculations to avoid ambiguity and confusion.
  • One participant expresses frustration over the lack of clarity in unit handling and suggests that not understanding units could hinder success in STEM fields.

Areas of Agreement / Disagreement

Participants generally agree on the need for clarity in unit assignments and the importance of dimensional analysis, but there is disagreement on the correctness of the calculations and how to properly express the final answer in terms of paperclips.

Contextual Notes

Participants highlight the confusion surrounding unit assignments and the implications of not properly expressing units in calculations. There are unresolved questions about the correctness of the numerical values presented and how they relate to the intended units.

rachelmaddiee
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Homework Statement
I need help with a question
Relevant Equations
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I’m trying to solve this question using the exact method in my book but I’m having trouble with setting this up. Here is my work**

The length of a football field (100 yards) needs to be converted to centimetersLength of paperclip = 3.2 cm long36 inches = 1 yardhow many paperclips in 100 yds = (unknown)yards —> centimeters
4467F949-66AF-4314-B37D-5553EAD2EB18.png
A43EC43C-223F-4C56-B924-9B91B0F4E447.jpeg
 
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What did you do so far to find a solution ?
 
Dimensional analysis
Convert the 100 yards to cm (there are 36 inches in a yard). Divide this by the length of the paperclip.
100 yards = 9144 cm
9144 cm/3.2 cm = 2,857.5 cm
 
rachelmaddiee said:
Dimensional analysis
Convert the 100 yards to cm (there are 36 inches in a yard). Divide this by the length of the paperclip.
100 yards = 9144 cm
9144 cm/3.2 cm = 2,857.5 cm
How do you get cm/cm = cm ? Get your units straight. That's ALWAYS something to be careful of
 
phinds said:
How do you get cm/cm = cm ? Get your units straight. That's ALWAYS something to be careful of
I converted 100 yds to cm
 
100 yds * 36 in/1 yd * 2.54cm/1 in = 9144 cm
9144 / 3.2 = 2857.5
Is this correct?
 
rachelmaddiee said:
100 yds * 36 in/1 yd * 2.54cm/1 in = 9144 cm
9144 / 3.2 = 2857.5
Is this correct?
UNITS, dammit, UNITS. :smile:
 
phinds said:
UNITS, dammit, UNITS. :smile:
Is it wrong?
 
It is meaningless as long as you don't put units on these numbers. They can be OK in terms of the numerical value that you are after, but you need to explicitly write 2857.5 of what.

If I tell you that I need 3.234 of a rope, would you know if I mean feet, meters, inches, yards, ells or fathoms?
 
  • #10
Borek said:
It is meaningless as long as you don't put units on these numbers. They can be OK in terms of the numerical value that you are after, but you need to explicitly write 2857.5 of what.

If I tell you that I need 3.234 of a rope, would you know if I mean feet, meters, inches, yards, ells or fathoms?
Cm?
 
  • #11
Yes, you've made it clear that you think your answer has come out in cm. What we've been trying to guide you to is that that is completely WRONG because you did not use units properly.
 
  • #12
phinds said:
Yes, you've made it clear that you think your answer has come out in cm. What we've been trying to guide you to is that that is completely WRONG because you did not use units properly.
Which part is wrong?
 
  • #13
rachelmaddiee said:
Which part is wrong?
The part where you assign units. Nowhere do you show paperclips. Your answer IS, after all, supposed to come out as a number of paperclips.

I ask you again, how can you have cm/cm = cm ? That's like say that 5 cm goes into 10 cm 2cm times. Ridiculous.
 
  • #14
100 yds * 36 in/1 yd * 2.54cm/1 in = 9144 cm
9144 / 3.2 = 2857.5 paperclips
 
  • #15
rachelmaddiee said:
100 yds * 36 in/1 yd * 2.54cm/1 in = 9144 cm
9144 / 3.2 = 2857.5 paperclips
No! Your calculations do NOT show paperclips and you have just arbitrarily converted a dimensionless number to "paperclips" without, apparently, any idea how you go there.

I'm done with this thread.
 
  • #16
phinds said:
No! Your calculations do NOT show paperclips and you have just arbitrarily converted a dimensionless number to "paperclips" without, apparently, any idea how you go there.

I'm done with this thread.
9144 cm / 3.2cm = 2857.5
I don’t understand what needs to be corrected. The units are confusing me.
 
  • #17
rachelmaddiee said:
9144 cm / 3.2cm = 2857.5
I don’t understand what needs to be corrected. The units are confusing me.
Oh, all right. I get impatient sometimes. You are going to have a hard time in any STEM field if you don't learn units.

ANSWER = 100 YARD x 36 INCH / YARD * 2.54 CM / INCH * 1 PAPERCLIP / 3.2 CM = 28575 PAPERCLIP

the YARD cancel, the INCH cancel, the CMs cancel, and you end up with ANSWER = # ofPAPERCLIPs

You should ALWAYS do a full exposition of units when doing STEM problems. Sometimes it will show you that you can't possibly have the right calculation.

If you think what I'm telling you is just trivial semantics, then I suggest you find a career as a shoe salesman or the like. Stay away from STEM fields.
 
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  • #18
phinds said:
Oh, all right. I get impatient sometimes. You are going to have a hard time in any STEM field if you don't learn units.

ANSWER = 100 YARD x 36 INCH / YARD * 2.54 CM / INCH * 1 PAPERCLIP / 3.2 CM = 28575 PAPERCLIP

the YARD cancel, the INCH cancel, the CMs cancel, and you end up with ANSWER = # ofPAPERCLIPs

You should ALWAYS do a full exposition of units when doing STEM problems. Sometimes it will show you that you can't possibly have the right calculation.

If you think what I'm telling you is just trivial semantics, then I suggest you find a career as a shoe salesman or the like. Stay away from STEM fields.
Thank you!
 
  • #19
phinds said:
Oh, all right. I get impatient sometimes
I sympathize. Happens to me too, sometimes. And then can easily forget a decimal point, just like ... :wink: hey !

(unless you do it on purpose, in order not to violate the PF rule about not handing over the corrrect answer directly :cool: )
 

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