Welcome to, METRIC PREFIX CONVERSIONS!
We will review the various metric prefixes, and then take a look at how to convert from one prefix to another.
So the prefixes are given here on the left, and each prefix has a symbol.
The base (circle) is the metric unit used with the prefix, which we will get to in a moment.
Each prefix represents a specific number, and that number can be expressed using a power of 10.
The base units are the metric units used to measure some quantity.
And so they can be attached to any prefix according to the quantity.
For example there can be a megagram, symbolized Mg, which is 10⁶ grams, or 1 million grams.
At the other end of the scale let’s say meter is our base unit.
So we could have a nanometer, which would be symbolized nm, which is 10⁻⁹ meters, or 1 billionth of a meter.
You can see that expressing the amount as a power of ten is much more convenient than writing out the zeroes in very large or very small numbers.
So any metric unit can be attached to any prefix which gives the unit a specific numerical value.
And we use the prefixes to represent any number. For example, 2.6 million grams would be 2.6 megagrams, or 2.6 Mg or 2.6 times 10⁶ grams or 2 million 6 hundred thousand grams.
18.2 billionths of a meter is 18.2 nanomters.
So now let’s take a look at how we can convert from one metric prefix to another.
To gain an easier perspective let’s put everything in a horizontal table and we will begin with meters and grams for our base units. The table allows for an easy view of each exponent, which we will need in the conversions.
For example, how many decigrams are in 2.6 kg. We will use a specific algorithm that uses the dimensional analysis set-up, as follows:
First step, write amount and unit given in the problem, then multiply by fraction with the given unit on bottom and wanted unit on top.
Now we need to fill in the numerical relationship between:
Decigrams and kilograms (which is where we now refer to the chart).
We put a 1 with the larger unit, which is kilograms,
and the smaller unit gets a power of ten,
determined simply by subtracting the exponents represented by the prefixes.
Kilo has an exponent of 3, Deci is -1.
And so the difference is 4, which becomes the exponent.
There is 10 to the 4th, or 10,000 decigrams for every 1 kilogram. With this set-up the kilograms cancel, leaving the desired unit decigram.
Do the math and we get 2.6 x 10⁴ dg.
We have determined there are 26,000 dg in 2.6 kg.
Click on this link if you need to review dimensional analysis beyond what is presented here.
Let’s try a problem where we are converting from a smaller unit, nm, to a larger unit, cm. The set-up is the same as before:
Write what is given, multiply by a conversion factor with given unit on bottom, wanted unit on top, larger unit gets 1.
The number for smaller unit is determined by subtracting the exponents represented by the prefixes.
nm cancels, leaving cm.
18.2 nm = 1.82 x 10⁻⁶ cm or 1.82 millionths of a cm.
But the purpose of scientific notation is to forget about dealing with lots of zeroes, so we can ignore this.
So any metric unit can be used with the prefixes:
E.g., liters or seconds or joules or pascals or Watts.
A common volume unit is milliliter, or 10⁻³ liters;
Or microseconds, a very short span of time;
Or terrajoules, a lot of energy;
Or kilopascals, a common unit of pressure in chemistry;
Or gigawatts, a billion watts.
If you’re a fan of "Back to the Future,"
you may remember Doc Brown speaking in terms of jigawatts to power his deLorean.
He may have pronounced it oddly, but jigawatts probably has more levity than gigawatts.
The last part of this video is concerned with unit conversions of squared and cubed unit lengths.
Length units such as meters or inches are interesting because squaring them gives us area and cubing them gives us volume. And so that changes the conversion because numerical relationships also have to be squared or cubed as well. Let’s look at a couple of examples.
What’s the relationship between square meters and square kilometers?
The initial set-up is the same as before:
Units given on bottom, units wanted on top.
What changes is their numerical relationship.
First we add the LINEAR relationship given by the table.
There are 10³ meters in a kilometer.
However, squaring the linear units requires that we square the numerical relationship.
There are 10³ squared m per km², a million square m in 1 square km.
Last, let’s look at cubed lengths, here, the relationship between cm cubed and dm cubed.
Note that a cubic decimeter is 1 liter. This is how the liter is defined.
The problem is how many cubic decimeters are in 44.5 cubic centimeters.
Again, same set up:
Using a conversion factor with given units on bottom, wanted on top,
with the larger unit getting 1.
Subtracting the exponents of the LINEAR relationship gives an exponent of 1.
But the units are cubed,
and so we cube the numerical relationship,
giving us 1 cubic dm for every thousand cubic cm.
44.5 divided by 1000 = 0.0445 cubic dm.
So for squared length, which is area,
the linear relationship is squared.
For cubed length, which is volume,
the linear relationship is cubed.
You should memorize the prefixes and the exponent each one represents. These prefixes are used extensively in science and you should have them in your head for immediate recall. You won’t get to use this chart on a test. Seeya!