Ex: Length Conversions:  Miles to Inches, Miles to Yards

we want to convert each measurement
around to three decimal places if needed we want to convert 3.5 miles two inches
and 15 miles two yards the conversions we need are given here below will
perform the conversions by multiplying by unit fractions looking at our first
example we want to convert 3.5 miles two inches so we’ll begin by writing 3.5
miles in fraction form which would be 3.5 miles over 1 and our goal is to convert this to inches. Looking at our conversions we’ll first convert miles to feet
using this conversion here. Notice miles is in the numerator here so we multiply it
by unit fraction where we’ll have miles in the denominator and feet in the numerator.
Notice this way the units of miles will simplify out. And the conversion is 5,280
feet equals 1 mile because these lengths are equal we’re multiplying by a fraction that’s
equal to 1. And notice how miles simplifies out. If we found this product
now, we can determine how many feet would be in 3.5 miles but since our goal is to
convert to inches will multiply it by another unit fraction to convert
feet to inches. And one foot is equal to 12 inches. Because you want feetto simplify out we’ll have feet in the denominator and inches in the numerator.
And again the conversion is 12 inches equals one foot. Notice how the units of feet simplify
out leaving us with inches. Now we’ll find this product to find the conversion.
But notice how the product of the denominators is just one we can simply
just find the product of the numerators. So we have 3.5 x 5280 x 12 so 3.5 miles is equal to 221,760 inches.
In our second example we want to convert 15 miles to yards and we use the same
process. We’ll begin by writing 15 miles in fraction form. We have 15 miles over
one. Notice how there’s not a direct conversion from miles to yards so begin
by converting again miles to feet and again our goal here is to convert
miles to yards. So for our first unit fraction because we want miles to
simplify out, we’ll miles in the denominator and feet in the numerator. So we have
5,280 feet in one mile. The units of miles simplifies out. Again our goal is
to convert to yards. Now will convert feet to yards. So we’ll multiply by another unit fraction. Because we want feet tosimplify out. Put feet in the denominator and yards in the
numerator the conversion is one yard equals 3 feet. The units of feet simplify
out, but notice how now we multiply the fractions we are going to have
denominator of three. Let’s show the next step down here. Multiply across the
numerator and multiply across the denominator. We know the units are yards
so the numerator would be 15 times 5280 which is 79200 and we can see our
denominator is 3. So we have 79200 / 3 yards. And now we’ll find this quotient
to determine the number of yards. 79200 divided by 3 is equal to 26400. Therefore 15
miles is equal to 26 thousand four hundred
yards. Both of these answers came out nice but notice how the directions to say if
needed round to three decimal places. I hope you found this helpful

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