# Dimensional analysis

## Homework Statement:

I need help with a question

## Relevant Equations:

N/A
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 centimeters

Length of paperclip = 3.2 cm long

36 inches = 1 yard

how many paperclips in 100 yds = (unknown)

yards —> centimeters

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BvU
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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

phinds
Gold Member
2019 Award
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

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?

phinds
Gold Member
2019 Award
100 yds * 36 in/1 yd * 2.54cm/1 in = 9144 cm
9144 / 3.2 = 2857.5
Is this correct?
UNITS, dammit, UNITS.

UNITS, dammit, UNITS.
Is it wrong?

Borek
Mentor
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?

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?

phinds
Gold Member
2019 Award
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.

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?

phinds
Gold Member
2019 Award
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.

100 yds * 36 in/1 yd * 2.54cm/1 in = 9144 cm
9144 / 3.2 = 2857.5 paperclips

phinds
Gold Member
2019 Award
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.

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.

9144 cm / 3.2cm = 2857.5
I don’t understand what needs to be corrected. The units are confusing me.

phinds
Gold Member
2019 Award
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.

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!

BvU