The metric system is universally used within the sciences.
However, some students really struggle with understanding how the metric system relates to scientific notation.
In this short tutorial, we’ll discuss metric prefixes,
and show how they can also be represented by both decimal numbers, and powers of 10.
Let’s begin with the metric staircase, which is a visual way of understanding the metric system.
This area here in the center of the staircase is what’s known as the base unit.
If you’re measuring length, this unit would be meters.
If you’re measuring volume, it would be liters,
and if you’re measuring mass, this would be grams.
For this animation, we’ll just go ahead and work with meters.
Notice that each step has a specific prefix.
Each of these prefixes can be associated with a specific number.
For example, the prefix deka means ten,
so a dekameter will be equal to ten meters.
As you move up the metric staircase, length measurements increase by factors of 10.
The prefix hecto means 100, so a hectometer would be equal to 100 meters.
Kilo means 1000, so a kilometer is equal to 1000 meters.
The prefix mega means million, so a megameter is a million meters
and a gigameter is equal to a billion meters.
Now, as you can see, these numbers can start to get really big,
so scientists have come up with a shortened form
to represent both the metric prefix and the number.
This involves scientific notation, or in this case what’s referred to as powers of 10.
For example, we already know that the prefix deka means 10.
The scientific notation for 10 is 10 to the first power, which is written like this.
The prefix hecto means 100, or 10 to the 2nd power.
Kilo means 1000, or 10 to the 3rd power.
Now pay attention when we get to mega, because mega is NOT 10 to the 4th power.
It’s 10 to the 6th power. We’ve skipped a few powers of ten.
Not every power of 10 has a metric
prefix associated with it.
So that’s important to know as you move up the staircase.
Giga, which means billion, can be referred to as 10 to the 9th power.
So how do you keep all these powers of ten straight, and know which decimal numbers they actually represent?
Well, the secret lies in keeping track of your decimal point.
Let’s go back to the base metric unit, which is always represented as 10 to the zero, or simply 1.0.
Notice where the decimal point is.
Now whenever you see a number with a power next to it,
that’s how many spaces to the right you move the decimal point.
Take deka for instance. Deka is 10 to the 1st power.
So you start with the base unit of 1.0, and then move the decimal point one space to the right.
So 10 to the 1st power is equal to 10.
Let’s try mega. Mega is 10 to the 6th power.
So start with 1.0, and then move the decimal point 6 spaces to the right.
So 10 to the 6th is equal to one million.
Let’s return to the base measurement of 10 to the zero, or 1.0 meters,
and then start moving down the metric staircase.
Notice that as you move down the staircase measurements decrease by factors of ten.
For example, the prefix deci means 1/10th, or 10 to the negative 1st power.
When you see that negative power, that simply means you need to move the decimal point to the left, instead of to the right.
So If you start with your base unit of 1.0,
and move the decimal point one space to the left, you end up with point one.
which is the same as one tenth.
Centi means 1 hundredth, or 10 to the negative two.
Milli means one thousandth, or 10 to the negative 3.
OK, now we skip a few powers of ten, and move on to micro,
which is 10 to the negative six, or one millionth - and nano,
which is 10 to the negative 9 or one billionth.
Let’s do a quick recap of what we’ve covered so far.
Remember that as you move up the metric staircase, measurements increase by factors of 10,
and as you move down the metric staircase, measurements decrease by factors of 10.
The power of 10 tells you how many places to move the decimal point.
A positive power tells you to move the decimal point to the right,
while a negative power means to move the decimal point to the left.