Ex: Metric Conversions Using Unit Fractions – Weight
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Welcome to three examples of converting weights using metric units. In a previous video, we
explained how we can use the table below in order
to perform conversions by moving the decimal
point to the left or right based upon the columns, but in these three examples, we’ll perform the conversions
using unit fractions. But let’s first look at our table. Notice the basic unit is the gram. The smallest unit in this
table is a milligram, which is equal to
one-thousandth of a gram, and the largest unit is a kilogram, which is equal to 1,000 grams. So for the first example, we’re going to convert
875 milligrams to grams. So notice the conversion that we’ll use is that one milligram equals 0.001 grams, or one-thousandth of a gram, and now we’ll set up 875
milligrams as a fraction. 875 milligrams over one, and we’re going to multiply
it by a unit fraction using this conversion. Because we want milligrams
to simplify out, we must have milligrams in the denominator and grams in the numerator. And now, using the conversion,
we have one milligram equals 0.001 grams. Notice in this form
milligrams simplifies out, so this product will
convert milligrams to grams. So we have 875 times 0.001. Notice how this is the same
as moving the decimal point to the left three times. We have 0.875 grams. Next, we’re going to convert
0.12 kilograms to centigrams, so we’re starting here and want to end up here with centigrams. And since grams is not
part of this conversion, we’ll have to first convert
to grams and then centigrams, so we’ll have to have two unit fractions. Notice from the table we know one kilogram equals 1,000 grams. And we also know that one centigram equals one-hundredth of a gram. And now we’ll set up our unit fractions. We’ll start with 0.12 kilograms over one. We’ll first convert the kilograms to grams using this conversion, so we must have kilograms
in the denominator, grams in the numerator, and, again, the conversion is 1,000 grams equals one kilogram. Notice how kilograms simplifies out. Now we’ll convert kilograms to centigrams with another unit fraction. We must have grams in the denominator and centigrams in the numerator. And, again, the conversion
is one centigram equals one-hundredth of a gram. Notice how gram simplifies out. So this is our conversion to centigrams. Notice how this would be, in the numerator we’d have 0.12 times 1,000 divided by 0.01 centigrams. Now let’s go to the calculator
to determine this value. 0.12 times 1,000 divided by 0.01. So this is equal to 12,000 centigrams. The last example, we’re going
to convert 258 milligrams to decagrams, so we’re converting milligrams
here to decagrams here. And, again, notice how the conversion does not involve grams, which means we’ll have to
have two unit fractions or two conversions to convert
milligrams to decagrams. So starting with milligrams,
notice that one milligram is equal to one-thousandth of a gram, and one decagram is equal to 10 grams. So, again, we’ll start
with the given units of 258 milligrams over one. Multiply by two unit fractions, one that will convert milligrams to grams. The second fraction will
convert grams to decagrams. So, first, we’ll have milligrams
in the denominator here. Converting to grams, so one milligram is equal to 0.001 grams. Notice how milligrams simplifies out. And now to convert grams to decagrams using this conversion here. Grams must be in the denominator, and decagrams must be in the numerator. Conversion is one decagram
is equal to 10 grams. The grams are now simplified out, and we’re left with decagrams. We have 258 times 0.001 divided by 10. So 258 times 0.001 divided by 10. So we have 0.0258 decagrams. Okay, hope you found these
three examples helpful.

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