Converting 100 Yards to Centimeters: Dimensional Analysis Explained

[rachelmaddiee]

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 centimetersLength of paperclip = 3.2 cm long36 inches = 1 yardhow many paperclips in 100 yds = (unknown)yards —> centimeters

 

[BvU]

PF guidelines require an effort from your part. We are not allowed to help otherwise.
What did you do so far to find a solution ?

 

[rachelmaddiee]

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]

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

 

[rachelmaddiee]

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

 

[rachelmaddiee]

100 yds * 36 in/1 yd * 2.54cm/1 in = 9144 cm
9144 / 3.2 = 2857.5
Is this correct?

 

[phinds]

100 yds * 36 in/1 yd * 2.54cm/1 in = 9144 cm
9144 / 3.2 = 2857.5
Is this correct?

UNITS, dammit, UNITS.

 

[rachelmaddiee]

UNITS, dammit, UNITS.

Is it wrong?

 

[Borek]

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?

 

[rachelmaddiee]

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]

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.

 

[rachelmaddiee]

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]

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.

 

[rachelmaddiee]

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

 

[phinds]

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.

 

[rachelmaddiee]

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.

 

[phinds]

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.

 

[rachelmaddiee]

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]

Oh, all right. I get impatient sometimes

I sympathize. Happens to me too, sometimes. And then can easily forget a decimal point, just like ... hey !

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