Basic Dimensional Analysis Question

[lolzwhut?]

1. Convert 1.2 in^2 to cm^2



2. 1 CM = 10^-2 and 1 inch = 2.54 centimeteres

The Attempt at a Solution

Can't we just do 1.2*2.54=3.048 and write that as our answer?

 

[lewando]

Can't we just do 1.2*2.54=3.048 and write that as our answer?

You could, but it would be wrong.

If 1 in = 2.54 cm, then, squaring both sides, 1² in² = 2.54² cm².

or simplified: 1 in² = 6.4516 cm². From this, we get the following facts:

1 = (1 in²) / (6.4516 cm²)

1 = (6.4516 cm²) / (1 in²)

Remember, you can multiply anything by 1 and it will not alter the value you are trying to convert. If you are starting with a value that has units of in² (as you are) then multiply that value by the ratio of the second equation (that ratio is equal to 1). The in² will cancel out leaving you with cm² in the numerator (which is what you want).

1.2 [STRIKE]in²[/STRIKE] * (6.4516 cm²) / (1 [STRIKE]in²[/STRIKE])

 

[tiny-tim]

hi lolzwhut?!

1. Convert 1.2 in^2 to cm^2

2. 1 CM = 10^-2 and 1 inch = 2.54 centimeteres

Can't we just do 1.2*2.54=3.048 and write that as our answer?

it's square inches!

 

[Borek]

Can't we just do 1.2*2.54=3.048 and write that as our answer?

To add to what lewando wrote - if you were not ignoring units, you would see that it is wrong.

Trying shortcuts when you don't understand what you are doing rarely works. Dimensional analysis strength relies on the fact that it not only gives correct results, but also gives signals if you get lost. However, it works only when you use both numbers and units in conversion coefficients.

 

[HallsofIvy]

1. Convert 1.2 in^2 to cm^2



2. 1 CM = 10^-2

Your first error is here. 1 cm= 10^-2 what?

and 1 inch = 2.54 centimeteres

The Attempt at a Solution

Can't we just do 1.2*2.54=3.048 and write that as our answer?

And, as others have pointed out, you simply dropped the units here and the units are the whole point of the problem.

 

[lolzwhut?]

You could, but it would be wrong.

If 1 in = 2.54 cm, then, squaring both sides, 1² in² = 2.54² cm².

or simplified: 1 in² = 6.4516 cm². From this, we get the following facts:

1 = (1 in²) / (6.4516 cm²)

1 = (6.4516 cm²) / (1 in²)

Remember, you can multiply anything by 1 and it will not alter the value you are trying to convert. If you are starting with a value that has units of in² (as you are) then multiply that value by the ratio of the second equation (that ratio is equal to 1). The in² will cancel out leaving you with cm² in the numerator (which is what you want).

1.2 [STRIKE]in²[/STRIKE] * (6.4516 cm²) / (1 [STRIKE]in²[/STRIKE])

Wow, so 7.74 cm^2 is what I'm getting.

Thanks for the help guys. I definitely won't forget my units this time xD But yeah, I got 7.74 cm^2.