We want to convert each measurement
and round to three decimal places if needed.
We want to convert 1,200 ounces to tons,
and 1.5 tons to ounces.
The conversions we need are provided here below,
to perform the conversions,
we'll multiply by unit fractions.
So to convert 1,200 ounces to tons,
we'll begin by writing 1,200 ounces in fraction form,
so we'll have 1,200 ounces over one,
which we want to convert to tons.
Looking at our conversions, notice how we'll first convert
ounces to pounds, and then pounds to tons.
To convert ounces to pounds,
we'll multiply it by unit fraction, where,
because we have ounces in the numerator here,
we'll put ounces in the denominator,
so that ounces will simplify out,
and we'll have pounds in the numerator,
and our conversion is one pound equals 16 ounces.
Notice how this fraction is equal to one
because the units are equal, but the unit of ounces
now simplifies out, and therefore if we found this product,
which would end up being a quotient,
would give us the number of pounds in 1,200 ounces.
But because our goal is to convert to tons,
we'll now convert pounds to tons,
by multiplying by another unit fraction.
We want pounds to simplify out,
so we'll put pounds in the denominator,
and tons in the numerator,
and our conversion is one ton equals 2,000 pounds.
Notice how the units of pounds simplifies out,
leaving us with tons.
Now we'll find the product of our fractions,
looking at the numerator, we just have
1,200 times one times one, so we have 1,200,
in our denominator we have one times 16 times 2,000,
which will be 32,000,
and now we'll find this quotient,
and if needed, round to three decimal places.
So we have 1,200 divided by 32,000,
which give us 0.0375 tons.
So the exact weight in tons is 0.0375,
but because our directions do say
round to three decimal places, we can also say,
this is approximately 0.038 ton.
Notice how the five in the fourth decimal place
indicates that we would round up,
so we increase the seven to an eight, if we do want to round.
So depending on the directions,
you can express your answer in one of these two ways.
Now for our second example, we want to convert
1.5 ton to ounces, we use the same process,
so we'll write 1.5 tons over one in fraction form,
multiply it by unit fractions to convert this to ounces.
We'll first convert tons to pounds,
and then pounds to ounces.
We want tons to simplify out,
so we'll write tons in the denominator,
and pounds in the numerator, and the conversion is
2,000 pounds equals one ton,
notice how tons simplifies out,
and now we'll convert pounds to ounces,
so we'll multiply it by another unit fraction.
We want pounds to simplify out,
notice here it's in the numerator,
so we'll have pounds in the denominator,
and ounces in the numerator, and our conversion is
16 ounces equals one pound.
Pounds is simplifies out, notice in this product,
the denominator is equal to one,
so we can just find the product of the numerators.
So we have 1.5 times 2,000 times 16,
which gives us 48,000,
and therefore 1.5 tons equals 48,000 ounces.
I hope you found this helpful.