 Measurement Unit Section 4: Converting
between measurement systems This next topic that we cover switching back and forth
between the English and Metric measurements. To do these conversions
you’ll need to refer to a table of conversion factors and use the
conversion factor fraction method. First example asks us to convert twenty
ounces into grams. If we refer to the table at the back of our book or a
standard conversion table. We’re gonna go fishing in that third column which is
English and Metric Conversion or equivalent values. And as we look under
the category of mass and weight we find a relationship between ounces and grams.
So to do our are conversion will take the given measurement expressed as a
fraction with a denominator of one. We will take that relationship between ounces
and grams and putting it in a conversion factor fraction such that the ounces
are going to cancel out. So the actual value is 1 ounce is equal to 28.3
grams. When we simplify are fraction we’ll cancel out common factors in the numerator and
the denominator leaving us to multiply the fraction which is multiplying the
numerator and the denominator which is one not affecting our value so the
equivalent of 20 ounces turns out to be 566 grams. The next problem asks us to
convert 3.4 kilograms to ounces. Again we look at our conversion table the third
column we’re looking for kilograms and ounces under the mass and
weight category that’s there. We take the given measurement we express it as a
fraction with the denominator of 1. We run into a little bit of a problem in
this one. There is no direct way to go from kilograms to ounces that means the
problem will require more than one conversion factor and here’s what it
looks like. When we look in the table we’re looking for a value that’s going
to cancel out our kilograms the given unit of measurement and we see from the
table that one pound is equivalent to 454 thousands of a kilogram. Placing that
kilogram value in the denominator its equivalent in the numerator we
essentially are multiplying by one. That allows our kilograms to cancel out and
before we do any calculation we’re not quite done. We need to now find something
that converts our current measurement which is in pounds into the desired unit
of measurement of ounces. So now we switch over to the English side of the
table and when we put our conversion factor together we want to be sure that
we have pounds in the denominator so it cancels out our current pound measurement. When
we look under weight on the English side since pounds is English and we’re headed
to ounces which is also English we find one pound is equal to 16 ounces. Here’s our second conversion factor
fraction. Pounds cancel out and now we’re ready to do the simplification.
Multiplying fractions you multiply your numerators together multiply all
denominators together and the last step would be to take that numerator product
and divided by the denominator product resulting in 119.8 ounces the
equivalent of the three and four tenths kilograms. In this next example we have
120 km/h and looking for an equivalent mile per hour. To do that we’re talking
about a rate here and the rate that we’re talking about is a distance per
unit of time. The time in both of these problems or
factors is hours so we’re okay there no conversion necessary but the numerator
the distance is kilometers and we need to express it in an equivalent mile
per hour. So we start with the given value 120 kilometers per one hour. We’re
looking on our conversion tables for a relationship between kilometers and
miles. On that third column which has the equivalent values in the English and
Metric system. We look under length. When we set up that conversion factor fraction
we want to make sure that the kilometer is in the denominator so that it will
cancel our current kilometers. From the table we find that one mile is equal to
1.61 kilometres. Placing them in the correct place or order allows us
to cancel out kilometers. Unit wise if we just look at this we have a mile per
hour that’s a pretty good indication that we have it set up correctly.
Simplifying the fraction by multiplying numerator values and multiplying
denominator values and then doing the division. It turns out that seventy four
and five tenths mile per hour is equivalent to the 120 km/h given speed. For
additional practice you have problems on page 24 and 25 on your textbook.