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Explain the rules for multiplication and division to convert units.
How do you know when to multiply and when to divide to convert units of measurement?
Write three to four sentences.
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Let's imagine that we measure some quantity 'A', and we find that this quantity is 'a' units, measured in the scale P.
(so, one unit in this scale is P, which we consider as a standard).
We want to express this quantity in the scale Q
(one unit in this scale is Q, which we consider as another standard).
We know that the ratio of quantities P and Q, , is 'k' (non-dimensional value).
Then the measure of the quantity 'A' in the scale Q (in terms of Q) is
conversion: 'a' units P ---> of units Q, or 'k*a' units Q. (1)
It is how conversion of units works.
Example.
Let 'A' be the quantity '3 hours', so it is a time interval.
The unit (= the scale) which we use for it now is P = 'one hour'.
We want to convert it to minutes.
So, the other scale is Q = 'one minute'.
We know that the ratio = = 60.
So, in this case 'k' = 60.
You know intuitively that 3 hours = 3*60 = 180 minutes.
Formula (1) converts in this case 3 hours into 3*60 = 180 minutes,
i.e. works in accordance with your intuition, precisely in a way as you expect it.
Usually, for simple units and simple everyday quantities, people make conversion
'in their mind' mentally without any problems.
For more complicated cases/quantities/conceptions, people use their professional expertise.
When they have enough expertise, they make conversion "without thinking"
and practically without errors even in complicated cases.
Exercises to check your understanding
(a) Convert $3.25 to cents.
(b) Convert 425 cents to dollars.