Dimensional Analysis: how big is 2000-in TV in feet, meters

[Mole]

Conversion factors... I can't understand them.

Example:
Frank has a 2000-inch television. How big is the television a) in feet and b) in meters?

(2000 in/1) * (1 ft/12 in) = 2000/12 ft = 166 2/3 feet?!

My guess is that Frank doesn't have such a big television. If 2000 inches is area, how do I deal with the conversion?

 

[Deleted member 4993]

Re: Dimensional Analysis

Conversion factors... I can't understand them.

Example:
Frank has a 2000-inch television. How big is the television a) in feet and b) in meters?

(2000 in/1) * (1 ft/12 in) = 2000/12 ft = 166 2/3 feet?!

Your conversion is correct - however, your doubt (concern) is well founded. Good job!!

My guess is that Frank doesn't have such a big television. If 2000 inches is area,

"inches" cannot be dimension of area - generally TV dimensions are expressed as the length of the diagonal.

how do I deal with the conversion?

 

[Mole]

Re: Dimensional Analysis

Conversion factors... I can't understand them.

Example:
Frank has a 2000-inch television. How big is the television a) in feet and b) in meters?

(2000 in/1) * (1 ft/12 in) = 2000/12 ft = 166 2/3 feet?!

Your conversion is correct - however, your doubt (concern) is well founded. Good job!!

My guess is that Frank doesn't have such a big television. If 2000 inches is area,

"inches" cannot be dimension of area - generally TV dimensions are expressed as the length of the diagonal.

how do I deal with the conversion?

Weird question, then.

A liter of gasoline in England costs 112.7 p. How much does one gallon cost in U.S. dollars? (Hint: 100 p = 1 pound, 1 pound = $1.75)

I'm stuck on this one. Do I convert the money or the liquid measurements first? Also, the conversion chart says that the conversion factor for 1 liter to gallons is .2642. How do I get a whole gallon out of that?

 

[Deleted member 4993]

Re: Dimensional Analysis

Start a new topic (thread) for new problem.

A liter of gasoline in England costs 112.7 p. How much does one gallon cost in U.S. dollars? (Hint: 100 p = 1 pound, 1 pound = $1.75)

I'm stuck on this one. Do I convert the money or the liquid measurements first?

No - certainly not. Convert pennies to dollar and convert liters to gallons

Also, the conversion chart says that the conversion factor for 1 liter to gallons is .2642. How do I get a whole gallon out of that?

\(\displaystyle 0.2642 \, gallon \, = \,1 \, liter\)

\(\displaystyle 1 \, gallon \, = \,\frac{1}{0.2642} \, liter\)

 

[Mole]

Re: Dimensional Analysis

Start a new topic (thread) for new problem.

A liter of gasoline in England costs 112.7 p. How much does one gallon cost in U.S. dollars? (Hint: 100 p = 1 pound, 1 pound = $1.75)

I'm stuck on this one. Do I convert the money or the liquid measurements first?

No - certainly not. Convert pennies to dollar and convert liters to gallons

Also, the conversion chart says that the conversion factor for 1 liter to gallons is .2642. How do I get a whole gallon out of that?

\(\displaystyle 0.2642 \, gallon \, = \,1 \, liter\)

\(\displaystyle 1 \, gallon \, = \,\frac{1}{0.2642} \, liter\)

I still don't understand. Is the first conversion 1 liter x something?

 

[Deleted member 4993]

Re: Dimensional Analysis

Start a new topic (thread) for new problem.

A liter of gasoline in England costs 112.7 p. How much does one gallon cost in U.S. dollars? (Hint: 100 p = 1 pound, 1 pound = $1.75)

I'm stuck on this one. Do I convert the money or the liquid measurements first?

No - certainly not. Convert pennies to dollar and convert liters to gallons

Also, the conversion chart says that the conversion factor for 1 liter to gallons is .2642. How do I get a whole gallon out of that?

\(\displaystyle 0.2642 \, gallon \, = \,1 \, liter\)

\(\displaystyle 1 \, gallon \, = \,\frac{1}{0.2642} \, liter\)

I still don't understand. Is the first conversion 1 liter x something?

\(\displaystyle 100 \,british\, pennies \, = \, 1.75 dollar\)

\(\displaystyle 1 \, british\, pennies \, = \, \frac {1.75}{100} dollar\)

\(\displaystyle 112.7 \, british\, pennies \, = \, 112.7 \cdot\frac {1.75}{100} dollar\)

 

[Mole]

Re: Dimensional Analysis

I do not know how to get a whole gallon from a liter, again.

1 liter x ?/1 liter = 1 gallon

 

[Deleted member 4993]

Re: Dimensional Analysis

Let me do a similar problem for you:

A liter of gasoline in France costs 1.30 euro. How much does one quart cost in U.S. dollars? (Hint: 1 euro = $1.60 and 1 liter = 1.0568 quarts)

\(\displaystyle 1.30 \, \frac{euro}{liter} \, = \, 1.30 \frac{euro}{liter} \, \cdot 1.60 \frac{dollar}{euro}\cdot \frac {1}{1.0568} \frac {liter}{quart}\)

\(\displaystyle = \, 1.30 \cdot 1.60 \cdot \frac {1}{1.0568} \frac {liter}{quart}\frac{euro}{liter}\frac{dollar}{euro} \,\)

\(\displaystyle = \, \frac{1.30 \cdot 1.60}{1.0568} \frac {dollar}{quart} \,\)

\(\displaystyle = \, 1.968205905 \frac {dollar}{quart} \,\)

\(\displaystyle = \, 1.97 \frac {dollar}{quart} \,\)

 

[Mole]

Re: Dimensional Analysis

Let me do a similar problem for you:

A liter of gasoline in France costs 1.30 euro. How much does one quart cost in U.S. dollars? (Hint: 1 euro = $1.60 and 1 liter = 1.0568 quarts)

\(\displaystyle 1.30 \, \frac{euro}{liter} \, = \, 1.30 \frac{euro}{liter} \, \cdot 1.60 \frac{dollar}{euro}\cdot \frac {1}{1.0568} \frac {liter}{quart}\)

\(\displaystyle = \, 1.30 \cdot 1.60 \cdot \frac {1}{1.0568} \frac {liter}{quart}\frac{euro}{liter}\frac{dollar}{euro} \,\)

\(\displaystyle = \, \frac{1.30 \cdot 1.60}{1.0568} \frac {dollar}{quart} \,\)

\(\displaystyle = \, 1.968205905 \frac {dollar}{quart} \,\)

\(\displaystyle = \, 1.97 \frac {dollar}{quart} \,\)

1.127 pound/liter * 1.75 dollar/pound * 1/.2642 liter/gallon ?

= 1.127 * 1.75 * 1/.2642 pound/liter * dollar/pound * liter/gallon
1.127 * 1.75/.2642 dollar/gallon ?

7.46 dollars per gallon

 

[Denis]

Re: Dimensional Analysis

1.127 pound/liter * 1.75 dollar/pound * 1/.2642 liter/gallon ?
= 1.127 * 1.75 * 1/.2642 pound/liter * dollar/pound * liter/gallon
1.127 * 1.75/.2642 dollar/gallon ?
7.46 dollars per gallon

CORRECT!!
Try and keep your teacher in "a good mood" (maybe extra marks!) by being CLEARER; something like:

1 gallon = 1 / .2642 = 3.7854 liters [1]

Liter cost = 112.7 / 100 = 1.127 pounds
1 pound = $1.75
So liter cost = 1.127 * 1.75 = $1.9725 [2]

So gallon cost = [1] * [2] = 3.7854 * $1.9725 = $7.4657... (OUTCH!)