Durham College - Unit Conversions: Example #6 - SALS tutorial

Hello. In this question, we are being to convert a length of 3.77 metres into a measurement
using feet and inches, and then round that number to the nearest 16th of an inch.
This is a bit trickier than the previous example, so I'll show you what my plan is before we
get started, and you can see an outline of what the steps are.
What we really want to do here is take a metric measurement using decimals, and convert it
to an Imperial measurement that - instead of using a decimal system - uses fractions.
In my opinion, the best plan for solving this problem is to first convert metres into feet,
where feet is given as a decimal.
Then leave the whole number part as feet, but take the left over part after the decimal
point and convert that into inches.
Then, again, keep the whole number part and leave that as inches, and take the decimal
portion and change that to the closes fraction over 16.
Those are the steps I'm going to follow, and if it sounds confusing then I'm sure it will
become more clear as you see me actually go through it step by step.
Step 1 is to convert 3.77 metres into feet. This is just like a regular unit conversion.
The first thing we need is a relationship between feet and metres.
It turns out that 1 metre is equal to 3.28 feet.
Now I want to take the 3.77 metres that we're starting out with and multiply it by a fraction
that has metres on the bottom, in order to make it cancel out.
So, I'm going to use 3.28 over 1 metre.
When I multiply that by 3.77 metres, the result is 3.77 times 3.28, which is 12.3656 feet.
At this point, I already know that this answer will have 12 feet in it, plus some number
of inches added to it.
I know that because it turned out that 3.77 metres is equal to 12 whole feet plus .3656
feet, which I just need to change to inches.
If the question was just asking for an answer in feet, I would be finished and the answer
would be 12.3656.
But it wanted the answer to be in feet and inches.
So, we now need to take the part of that answer that was after the decimal and convert that
into inches.
The part after the decimal was .3656 feet and I need a conversion factor to change that
to inches.
I know that 1 foot is equal to 12 inches - 12 inches make up 1 foot.
So, I can multiply the .3656 feet by 12 inches over 1 foot and that will make the feet units
cancel.
The result is .3656 times 12 is 4.3872.
Now we're one step closer because now we know that the 3.77 metres we started out with is
equal to 12 feet and 4.3872 inches.
But the question also wanted the answer to be rounded to the nearest sixteenth of an
inch.
That means we need to take the part to the right of the decimal - the inches this time
- and change it to a fraction where the denominator is over 16.
So I'll just make a note that 4 is the number of whole inches in the answer, and we need
to convert the part to the right of the decimal to a fraction over 16.
The quickest way to do this is the multiply .3872 by 16, and what we're really doing here
is changing the denominator by multiplying the top and the bottom by 16.
If you recall, one of the rules for fractions is that you can multiply the top and the bottom
by the same number to find an equivalent fraction with a different denominator.
Usually, that comes in handy when we're trying to add fractions together by finding a common
denominator.
This time, I want to take 0.3872 over 1 and multiply it by 16 over 16.
This gives a result of 6.1952 over 16, which we round down to 6 over 16.
So now we know that that .3872 inches that was left over is actually equal to 6 sixteenths
of an inch, so that will be part of the answer.
So putting it all together, we had 12 feet and 4 and 6 sixteenths inches and that is
the final answer.
Therefore, I can write that 3.77 metres is the same as 12 feet, 4 and 6 sixteenths inches,
and there is just another way of writing it that you might see.
Now, the reason you might have to do this calculation in the first place is if you had
to measure out this distance on a ruler or a tape measure that marked like this one.
On this ruler, the numbers represent inches, and there are 16 lines on each inch, so each
line or tick mark between them represents a sixteenth of an inch.
Now, see if you can figure out where 4 and 6 sixteenths inches would be on this ruler...
If this is where you thought it was, then you're absolutely right.
This is exactly 6 tick marks after the four, so this arrow shows where you would measure
up to if you wanted to draw a length of 4 and 6 sixteenths inches.