This video is about scientific notation and metric multipliers.
We will discuss why scientific notation is used, see how scientific notation looks like,
discuss examples of how to convert to and from scientific notation, briefly talk about
what metric multipliers are, and finish up with some examples about using metric multipliers.
Let's just start by saying that scientific notation means exactly the same thing as standard
form.
The expression standard form is mainly used in a UK and a few other places.
So why do we use scientific notation?
Simply put, scientific notation is used to express very large and very small numbers.
Its name comes from the fact that it is in the sciences where we come across such numbers.
For example, the distance between stars is very large while the diameter of an atom is
really small.
Let's see how scientific notation looks like.
Scientific notation is a number between 1 and 10 multiplied by 10 to an integer or
whole number power.
Let's see two examples of numbers that are written in scientific notation.
You can see that both 7.1 and 1.836 are numbers between 1 and 10, and they are multiplied
by 10 to the power of 4 and 10 to the power of negative 2 respectively.
Note that both 4 and negative 2 are integers.
Just a side note that scientific notation has a few other technical details, but I won't
go into these because they are not really relevant to what we are covering in this video.
Next we'll see how to work with scientific notation.
We'll convert these four numbers.
Let's start by moving the decimal point to get a number between 1 and 10.
This gives us 4.933867.
In scientific notation, we have to multiply this by 10 to a certain power.
To find the power, we have to see by how many places we move the decimal point and in which
direction.
Here, we move the decimal point by 4 places to the left.
Since we moved the decimal place to the left, the power of 10 will be positive 4.
For the next number, we will move the decimal point 7 places to the right.
This gives us 1.306.
Let's figure out the power of 10 in the multiplication.
Since here, we move the decimal point by 7 places to the right, the power of 10 will
be negative 7.
An important point is that when we move the decimal point to the left, we get a positive
power and when we move it to the right, we get a negative power.
Another way to remember this is that when we convert a large number into scientific notation,
the power will be positive and when we convert a small number into scientific notation, the
power will be negative.
Next let's see how to convert from scientific notation to a regular number.
We will start by writing down 7.1 and since we have a positive 4 in the power of 10 and
we are converting from scientific notation to a regular number, we will move the decimal
point 4 places to the right.
To finish up, we will fill in the empty spaces with zeros, so we get 71,000.
For the next number, we will also start by writing down 1.836 and since here the power
of 10 is negative 2, we will move the decimal point 2 places to the left so it ends up here.
Then we'll fill in the empty space with a zero and I will put another zero in front
of the decimal place and get 0.01836.
You can also give your answer as 0.01836.
Let's continue with metric or SI multipliers.
Note that another name for metric multipliers is prefixes.
Metric multipliers are used with units and similarly to scientific notation, they help
abbreviate large and small numbers.
Let's see a few examples of metric multipliers.
Mega denoted with capital M stands for 10 to the power of 6 and everyday use of this
is in megabytes, which basically means 10 to the power of 6 or 1 million bytes.
Kilo abbreviated with the letter K stands for 10 to the power of 3 and can be seen in
kilogram.
Centi abbreviated with lowercase c stands for 10 to the power of negative 2 and is found
in centimeters and milli lowercase m is 10 to the power of negative 3 and can be seen
in millimeters or milliliters.
Finally, let's see how metric multipliers are used.
Before discussing examples, just a quick note that metric multipliers are found on page 5
of the data booklet, so there's no need to memorize them.
Let's see two examples of using metric multipliers.
We'll start by writing down 28000.
Millie stands for 10 to the power of negative 3, so here we get a multiplication by 10 to
the power of negative 3, so we have to move the decimal point from the end of the number
three places to the left.
This gives us 28 meters.
Let's write down 7.53 and since mega stands for 10 to the power of 6, here we get times
10 to the power of 6.
Let's again write down 7.53 and move the decimal point six places to the right.
After filling in the empty spaces with zeros, we end up with 7,530,000 watts.
Let's summarize this video.
We learned that scientific notation is used to abbreviate large and small numbers, so
that scientific notation is a number between 1 and 10 multiplied by 10 to an integer or
whole number power.
Through examples, we discussed that when converting a large number into scientific notation,
the power of 10 is positive and when converting a small number, the power of 10 is negative.
We also learned that metric multipliers are used with units to abbreviate large and small
numbers and we concluded that there is no need to memorize the metric multipliers because
they are found on page 5 of the data booklet.
This completes our discussion of scientific notation and metric multipliers.
In the next video, we will talk about significant figures.