# Problems converting quantities

1. Jun 1, 2009

### SirNostalgic

i have problems converting quantities, like for example Km/h to metres per second, or Days to seconds. I realise it involves multiple multiplications or division but for some reason i still have trouble with this relatively simple concept. In some cases, i even get the final answer wrong because i've made a mistake in my conversion.

could anyone possibly show me their methods of conversion and any tips that could help me as i have an exam soon and don't want to waste time thinking of wether it requires me to times or divide while i sit the exam.

Thanking you. SN

2. Jun 1, 2009

### CompuChip

There are two ways I often use.
One of them is including the units in my calculation, as if they were just variables. Then you can just simplify them using your algebra knowledge. For example, let me convert 50 km/h to m/s. I know there are 1000 m to a km and 3600 s to an h. Therefore,
1 = 1000 m / km;
1 = 3600 s / h.

I want to get rid of km and h and get m and s in the final answer. So I can combine them like this:

(50 km/h) * (1000 m/km) = 50000 (km*m)/(h*km).
Treating "km" as a single quantity, it is in the denominator and the numerator, so it cancels out: (50 km/h) * (1000 m / km) = 50000 m/h. To get rid of "h" I need to divide:
(50000 m/h) / (3600 s/h) = (50000/3600) (m/h)/(s/h) = (50/3.6) (m*h)/(h*s) = (50/3.6) m/s.

The other way I tend to use is a table (I don't know what it's called, I tend to call it a cross or ratio table). Put three knowns in a table, then multiply diagonally and divide vertically or horizontally. For example, convert 50 km/h to m/s.

Note that 1 km = 1000 m and 1 hour is 3600 seconds. So 50 km/h means: 50000 meters in 3600 seconds. Now the velocity in m/s says how many meters are crossed in one second. So in the table
Code (Text):

50000 m | 3600 second(s)
?   m | 1 second(s)

we want to know what is on the position of the question mark. You can start in the left top corner, multiply diagonally and then divide vertically. Or you can start in the right bottom corner, multiply diagonally and then divide horizontally. (Or in some other way). Let me do the former: start at 50000, multiply by 1, then divide by 3600. The question mark is 50000*1/3600 = 50/3.6 m.
So 50000 m in 3600 s corresponds to 50/3.6 m in 1 s. Hence 50 km/h ~ 50/3.6 m/s.

3. Jun 2, 2009

### SirNostalgic

i see what you've done and i have to say that is a useful way to tackle the quantities, i liked in particular what you did in those last few steps, i realised that i can transpose it around to get the answer i need. Thanks alot, ill give it a try once my I.T sac is done

4. Jun 2, 2009