Basic conversion question physics 101

[vysero]

A "gry" is an old English measure for length, defined as 1/10 of a line, where "line" is another old English measure for length, defined as 1/12 inch. A common measure for length in the publishing business is a "point", defined as 1/72 inch. What is an area of 0.50 gry^2 in points squared (points^2)?

I suck at math and am having trouble figured out how to deal with the square units.

 

[rock.freak667]

Once you write down how much 1 gry is, the squaring just becomes as simple as

1 cm = 10^-2 m

square both sides

1 cm² = 10^-4 m²

 

[vysero]

Wait it tells me what 1 gry is, it is = 1/10 of a line. I am confused should I just figure out how many gry's are in a point and then set that conversion = to .50 gry^2?

 

[vysero]

I did not want to start a whole new thread but I have stumbled on another basic conversion problem. Do not get me wrong I am still having trouble with the first but here is the second problem.

A tourist purchases a car in England and ships it home to the United States. The car sticker advertised that the car"s fuel consumption was at the rate of 40 miles per gallon on the open road. The tourist does not realize that the U.K. gallon differs form the U.S. gallon: 1 U.K. gallon = 4.5460900 liters 1 U.S. gallon = 3.7854118 liters.
For a trip of 750 miles (in the United States), how many gallons of fuel does (a) the mistaken tourist believe she needs and (b) the car actually require?

The reason this is throwing me off was because I thought figuring your gallons was as simple as dividing your mileage by your mpg... like 750miles/40mpg= 18.75gal

So was I right? I thought I mite be so then here is what I did to figure the difference...

4.5460900-3.7854118 = .7606782

I then converted that into gallons and said that she needed .200950016 extra gallons of gas... I think I messed this problem all up thought. Please help.

 

[rock.freak667]

Wait it tells me what 1 gry is, it is = 1/10 of a line. I am confused should I just figure out how many gry's are in a point and then set that conversion = to .50 gry^2?

You want to convert gry^2 to point^2, so yes, you will need to find how much 1 gry is equal to in point.

It says 1 gry = 1/10 line

It also tells you how much a line is. So keep going until you get 1 gry = point.

 

[vysero]

Ok well I am not sure if I am correct but I came up with .0115740741 gry's/point does that sound right and if it is what do i do next? Is this the part where I set that = to .50 gry^2?

 

[Clever-Name]

That isn't quite right, can you show your calculation?

 

[vysero]

Sure I went:

gry / 1/10line x line / 1/12in x 1/72in / point = (1/72) / (1/10)(1/12)= .0115740741 gry's/point

I am not sure where I went wrong...

 

[Clever-Name]

Ah, simple calculator error. You calculated [(1/72)/(1/10)] X (1/12)

You need to calculate

(1/72) / [(1/10)x(1/12)]

Then your answer is correct

 

[vysero]

Ok so 1.666666667 gry's/point does that look right? Now do I have to set this equal to .50 gry^2?

 

[Clever-Name]

How would that help you? You're saying:

1.6666666 gry / point = 0.50 gry^2

I don't see the logic in that.

You want 0.5 gry^2 in point^2. First figure out what 1 gry equals in terms of points, i.e.

1 gry = x points

Then calculate out 0.5 gry^2

 

[vysero]

Hmm so if 1.666666667 gry's/point then 1 gry = .59999999988 points right? So now I am confused my what you mean when you say calculate out 0.5 gry^2.

Like take the square root of that or do you mean change it too .25 gry's? I am having trouble seeing what I should do next my logic sucks.

 

[Clever-Name]

Round that up to 1 gry = 0.6 points. It's the accurate answer.

Perhaps we should ask the question like this.

Calculate 0.5 x (1 gry)^2

What is that in points?

 

[Nessdude14]

Ok so 1.666666667 gry's/point does that look right? Now do I have to set this equal to .50 gry^2?

$\displaystyle (1.667\frac{gry}{point})^{2}=2.778\frac{gry^{2}}{point^{2}}$

Using that conversion factor, it should be easy for you to convert from gry² to point². Hope that helps.

 

[vysero]

Does 5.56 point^2 sound right?

 

[Nessdude14]

Does 5.56 point^2 sound right?

Always make sure you work through the units. Here's what you did:
$\displaystyle 2.778\frac{gry^{2}}{point^{2}}×\frac{1}{0.5 gry^{2}}=5.56\frac{1}{point^{2}}$

What you want to do is:
$\displaystyle \frac{point^{2}}{gry^{2}}×gry^{2}$

Here's another hint: you can flip the conversion factor to read:
$\displaystyle \frac{1}{2.778}\frac{point^{2}}{gry^{2}}$

 

[vysero]

So 1.4 point^2? I am sorry I am so confused for some stupid reason. Or maybe .6945 point^2?

 

[vysero]

1 point^2/2.778 gry^2 x .5 gry^2/1 = .19 point^2

I feel like I am just grasping at straws here guys maybe I just shouldn't be doing this stuff.

 

[Nessdude14]

Nevermind this post

 

[Nessdude14]

I think it's too late for me to be doing math. Don't mind my previous post, here's how you do the conversion:

$\displaystyle 0.5gry^{2} × \frac{1}{2.778}\frac{point^{2}}{gry^{2}} = 0.18 point^{2}$

Notice that gry² cancels to leave only point² in the numerator.