Unit Conversions Example #6 – Mixed Units

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.

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