Welcome to lesson on metric conversions. The metric system originated in Europe
around eighteen hundred, and was quickly adopted around the world as a standard system of
measurement. In fact the U.S. is the only industrialized country that does not use
the metric system as its official measurement system, even though there are
metric units utilized in the U.S. for various things.
The strength of the metric system is that it is based on powers of ten
as you can see in the chart below. Looking at this row we have one thousand times
the base, one hundred times the base, ten times the base and so on.
Prefixes are the same for each power of ten above, or below the base unit. So the
metric system has three base units, meter for length, liter for capacity and gram
for weight. And the prefix indicates how that unit relates to the base unit.
Looking at the far left,
if the prefix is kilo, the unit would be one thousand times the base unit.
Meaning if we have a kilometer, or kilometer, a kilogram, or kiloliter,
the unit is one thousand times the base unit. Looking at the far right,
if we have a prefix of milla, or milli, then the unit is one thousandth times the base.
So if we have millimeter, milliliter, or milligram, the unit is one thousandth times the
base unit. This table can be used for conversions
however, in this lesson, we will focus on performing conversions using unit fractions.
But we will still use a table to verify the conversions.
To form our conversions
using unit fractions, we'll use these common conversions for length, weight and
volume. In the first example, we need to determine how many milligrams in
four thousand, two hundred grams.
We first write four thousand two hundred grams as a fraction with a denominator of one.
So we have four thousand, two hundred grams over one times, now we'll form a unit fraction that will convert
grams to milligrams.
So looking at the conversions,
one gram equals one thousand milligrams. And because we want grams to simplify out of
this product, grams must be in the denominator. And therefore, milligrams
will be in the numerator. And therefore, the unit fraction will be one thousand
milligrams divided by one gram.
Notice how this fraction is equal to one, so we're not changing the value
we are only changing the units. Notice the units of grams simplify to one. And we're
left with four thousand, two hundred times one thousand milligrams,
which gives us four million two hundred thousand milligrams in four thousand,
two hundred grams.
Let's verify this conversion by looking at the table.
We are converting from grams, which is in the middle column, to milligrams, which is
on the far right. To move from the column from grams to milligrams,
we must move one, two, three columns to the right. Which means if we move the
decimal point to the right three times in four thousand, two hundred, we can
determine how many milligrams in four thousand two hundred grams. So starting
with four thousand, two hundred, the decimal is to the right of the zero.
If we move it right three places, one, two, three
fill in the missing digits with zeros. Notice how we do get four million, two
hundred thousand, which is the number of milligrams in four thousand, two hundred grams.
Let's look at our second example. We're asked to determine how many meters in forty-five
centimeters. So beginning with forty-five centimeters as a fraction with the
denominator of one. We multiply by a unit fraction that will convert centimeters to meters.
Looking at our conversions, one meter equals one hundred centimeters.
Because we want centimeters to simplify out of this product, centimeters must be
in the denominator and therefore, meters will be in the numerator. And again
because one meter equals one hundrd centimeters, our unit fraction is one meter divided by
one hundred centimeters. The units of centimeters simplify to one.
Multiplying, we have forty-five over
one hundred, or forty-five hundredths meters.
We could simplify this fraction to nine-twentieths, but instead, let's write this as a
decimal. Forty-five hundredths is equal to zero point four five, and the units are meters.
So now we know
forty-five centimeters equals zero point four five meters. Again let's verify this
using the table.
We first locate centimeters in the table, which is here. And then locate meters, which
is in the middle. To move from the column of centimeters to the column of meters,
we have to move one, two columns to the left. And therefore, to determine how many
meters in forty-five centimeters, move the decimal point in forty-five to the left
two places.
So right now the decimal point is to the right of the five, moving it left two places,
one two. We get point four five, or zero point four five, which is the number of meters in forty-five centimeters.
Let's look at the last example. We want to know how many kiloliters are in
seven million, two hundred thirty-six thousand, one hundred thirty-seven milliliters.
Notice how here we're using a lowercase l and the table uses capital L's. Both
forms are accepted.
We first write the value as a fraction with a denominator of one.
We do not have a conversion directly from milliliters to kiloliters
and therefore, we'll have to use two unit fractions.
Looking at the conversions, we'll first use the conversion, one liter equals one thousand milliliters.
Because we want milliliters to simplify out, we must have milliliters
in the denominator, and we'll have liters in the numerator. The conversion
is one liter equals one thousand milliliters and therefore, the fraction is one divided by one thousand
milliliters. Notice the units of milliliters simplify to one. And now,
we'll covert liters to kiloliters. One kiloliter equals one thousand liters.
We want liters to simplify out and therefore, liters must be in the
denominator and kiloliters must be in the numerator. Our unit fraction will be one
kiloliter divided by one thousand liters.
When we multiply notice how we'll have seven million, two hundred thirty-six thousand, one hundred thirty-seven divided by one million.
And this quotient is equal to seven point two three six one three seven kiloliters.
Let's confirm this conversion using our table. We are converting milliliters to
kiloliters,
so we'd first locate milliliters, which is in the rightmost column, and then we locate
kiloliters, which is in the leftmost column. To move from milliliters to
kiloliters, we have to move
one, two, three, four, five, six columns to the left, which means,
we can determine the number of kiloliters in seven million, two hundred thirty-six thousand, one hundred
thirty-seven millimeters
by moving the decimal point to the left six places.
To start, the decimal is to the right of the seven. Moving is left six places we have one,
two, three, four, five, six.
Which gives us seven point two three six one three seven kiloliters
which is the correct conversion. So whether we use unit fractions or the table,
of course the conversions are the same.
I hope you found this helpful.