more conversion

I'm being introduced to conversions this week in my hydrology course after having been away from math for quite some time (lol). So if these questions seem like a joke (too easy) then at least you know...:)

What is the sum of the following measurements? 35.0 ft, 1.35 ft, 72 in., 48.69 ft expressed a) in ft b) expressed in m.

I need to convert 72 in to ft to get similar units, so my total is 91.04 feet.

So I have a rule telling me that the absolute precision of a sum equals the absolute precision of the least absolutely precise number involved (would I keep my final answer as 91.04 ft then?)

Conversions are confusing me going from one unit to another, and my book only gives one example of miles to meters, showing the work. If anyone could show work on part b it would help me out (I realize there are many websites that will do conversions for you but they don't show how the answer was arrived at)

Quote:

Originally Posted by kas34

I'm being introduced to conversions this week in my hydrology course after having been away from math for quite some time (lol). So if these questions seem like a joke (too easy) then at least you know...:)

What is the sum of the following measurements? 35.0 ft, 1.35 ft, 72 in., 48.69 ft expressed a) in ft b) expressed in m.

I need to convert 72 in to ft to get similar units, so my total is 91.04 feet.

So I have a rule telling me that the absolute precision of a sum equals the absolute precision of the least absolutely precise number involved (would I keep my final answer as 91.04 ft then?)

Conversions are confusing me going from one unit to another, and my book only gives one example of miles to meters, showing the work. If anyone could show work on part b it would help me out (I realize there are many websites that will do conversions for you but they don't show how the answer was arrived at)

here are two main ways to do conversions:

method 1.

simply replace the unit of measurement you don't want, with it's conversion in the measurement you do want and simplify

example. say we want to convert 32 feet to inches.

we know that 1 ft = 12 inches. that is, wherever i see the unit "ft" i can replace it with "12 in"

so, 30 ft = 30 (12 in) = 30*12 in = 360 in

method 2.

we relate the conversion factors in terms of ratios, in such a way that the units we don't want cancel out, and the units we do want stay.

lets do the previous example using this method.

we know 1 ft = 12 in. to put this in a ratio, we can write it as either $\frac {1 ~\text{ft}}{12~\text{in}}$ or $\frac {12 \text{ in}}{1 \text{ ft}}$ , depending on what we want to convert from.

lets say we want to, again, convert 30 ft to inches, so we write down 30 ft

$30 \text{ ft}$

now we want to multiply this by one of the ratios above to get it in inches. since we want the ft units to cancel out and the inches unit to stay, i want the ft unit in the denominator to cancel the ft from the 30 ft, and leave the in unit in the numerator. that is, we write

$30 \text{ ft} \times \frac {12 \text{ in}}{1 \text{ ft}}$

now the ft unit cancels, and we are left with

$30 \times \frac {12 \text{ in}}1 = 360 \text{ in}$

and that's it. now try to do the problems yourself and post your answers. note that if you are adding quantities, you need them to be in the same units. so if you want to sum 35.0 ft, 1.35 ft, 72 in., and 48.69 ft, you must first convert that 72 in to ft. then add them. then you can convert the answer to meters for part (b)

good luck!

wow thanks. i can't really post my answer for b (you see i worked out a in my original post) because I don't know how to type my ratios like everyone else. i am doing method two, where you cross out this and that until you get to the answer. thanks for the explanation though