Let's get started and learn how to convert
Let's get started and learn how to convert

percentages to decimals.
percentages to decimals.

And if we have time maybe we'll also learn how to convert
And if we have time maybe we'll also learn how to convert

decimals into percentages.
decimals into percentages.

So let's get started with what I think is a problem you
So let's get started with what I think is a problem you

probably already know how to do.
probably already know how to do.

If I said I have 50%.
If I said I have 50%.

I don't know if I wanted to write that thick,
I don't know if I wanted to write that thick,

but we'll go with it.
but we'll go with it.

Actually, let me change it to a thinner one.
Actually, let me change it to a thinner one.

And I want to turn that into a decimal.
And I want to turn that into a decimal.

Well you probably already have a sense of what
Well you probably already have a sense of what

decimal represents 50%.
decimal represents 50%.

If I told you we're having a sale and it's 50% off you know
If I told you we're having a sale and it's 50% off you know

that's roughly half off, or another way, how do you
that's roughly half off, or another way, how do you

say half as a decimal?
say half as a decimal?

Well that's the same thing as 0.5 So you might have known
Well that's the same thing as 0.5 So you might have known

that in your head, but is there a system for being able to
that in your head, but is there a system for being able to

convert this 50% to 0.5?
convert this 50% to 0.5?

Well, it turns out it's pretty straightforward.
Well, it turns out it's pretty straightforward.

All you do is you say-- whatever percentage it is,
All you do is you say-- whatever percentage it is,

that's the same thing as the number over 100.
that's the same thing as the number over 100.

And 50/100 is the same thing as 5/10 or 0.5.
And 50/100 is the same thing as 5/10 or 0.5.

Now even a simpler way of converting percentage to
Now even a simpler way of converting percentage to

decimals and, I think, you're going to realize converting a
decimals and, I think, you're going to realize converting a

percentage to a decimal or the other way around, you can
percentage to a decimal or the other way around, you can

pretty much do it in your head.
pretty much do it in your head.

If I say, let's say 50-- and I'm just going to add one
If I say, let's say 50-- and I'm just going to add one

decimal of accuracy here just to show you a point-- 50.0%.
decimal of accuracy here just to show you a point-- 50.0%.

If I want to convert that 50.0% into a decimal, all I do is I
If I want to convert that 50.0% into a decimal, all I do is I

get rid of the percent sign.
get rid of the percent sign.

So I'll do it here.
So I'll do it here.

50.0%.
50.0%.

I get rid of the percent sign and I take the decimal point
I get rid of the percent sign and I take the decimal point

and I move it over two spaces to the left.
and I move it over two spaces to the left.

So I say 1, 2.
So I say 1, 2.

So this is where the new decimal is.
So this is where the new decimal is.

So this equals we could say 0.500.
So this equals we could say 0.500.

So 50.0% is equal to 0.500.
So 50.0% is equal to 0.500.

And of course, these last two 0's really don't mean anything
And of course, these last two 0's really don't mean anything

for our purposes, so we'll get rid of them.
for our purposes, so we'll get rid of them.

So that's the same thing as 0.5 or just 0.5.
So that's the same thing as 0.5 or just 0.5.

50% equals 0.5.
50% equals 0.5.

So you're probably saying, well, sure.
So you're probably saying, well, sure.

That looks easy, but what if the problem gets
That looks easy, but what if the problem gets

a little harder?
a little harder?

50% I could have done in my head.
50% I could have done in my head.

So let's try some, I would say, slightly harder problems.
So let's try some, I would say, slightly harder problems.

If I were to tell you that-- let's say 16.32%.
If I were to tell you that-- let's say 16.32%.

Well, let's just do it the way I just showed you.
Well, let's just do it the way I just showed you.

I'll rewrite it down here.
I'll rewrite it down here.

16.32%.
16.32%.

So if we get rid of the percent sign, scratch it out, we just
So if we get rid of the percent sign, scratch it out, we just

have to move the decimal over two spaces to the left.
have to move the decimal over two spaces to the left.

So 1, 2.
So 1, 2.

This is the new place for the decimal.
This is the new place for the decimal.

That decimal goes away.
That decimal goes away.

So it's 0.1632 is equal to 16.32%.
So it's 0.1632 is equal to 16.32%.

I think you might be getting the idea now.
I think you might be getting the idea now.

Let me do another one in green.
Let me do another one in green.

Let's say I had-- and this one actually confuses
Let's say I had-- and this one actually confuses

a lot of people.
a lot of people.

Let's say I had 0.25%.
Let's say I had 0.25%.

So the important thing to remember is, I'll rewrite here.
So the important thing to remember is, I'll rewrite here.

0.25-- and maybe I'll write 00.-- And you're probably
0.25-- and maybe I'll write 00.-- And you're probably

wondering why I'm doing this, but I think you'll see in a
wondering why I'm doing this, but I think you'll see in a

second why I wrote that leading 0 there even though it doesn't
second why I wrote that leading 0 there even though it doesn't

seem to add much to it.
seem to add much to it.

00.25%.
00.25%.

Well, what's the system I just showed you?
Well, what's the system I just showed you?

You get rid of the percent sign and you move the
You get rid of the percent sign and you move the

decimal over 1, 2 spaces.
decimal over 1, 2 spaces.

So that equals 0.0025.
So that equals 0.0025.

So 0.25% is equal to 0.0025.
So 0.25% is equal to 0.0025.

And you could put a leading 0 here if you want.
And you could put a leading 0 here if you want.

Actually, I should probably tell you to always do that
Actually, I should probably tell you to always do that

because it makes it easier to read.
because it makes it easier to read.

So 0.25% is equal to 0.0025.
So 0.25% is equal to 0.0025.

And I want to just contrast that with 25%.
And I want to just contrast that with 25%.

25%, what do you think that equals?
25%, what do you think that equals?

Well.
Well.

you do the same thing that we've been doing.
you do the same thing that we've been doing.

You get rid of the percent sign and you move the decimal space.
You get rid of the percent sign and you move the decimal space.

In this case-- actually, let me leave that there.
In this case-- actually, let me leave that there.

I'll just rewrite it here.
I'll just rewrite it here.

25%.
25%.

And you're probably saying, where is the decimal in this?
And you're probably saying, where is the decimal in this?

Well, the decimal is after the number because that 25% is
Well, the decimal is after the number because that 25% is

the same thing as 25.0%.
the same thing as 25.0%.

So if we get rid of the percent sign, we move the decimal over
So if we get rid of the percent sign, we move the decimal over

two spaces to the left, and that equals 0.25 as a decimal,
two spaces to the left, and that equals 0.25 as a decimal,

or 0.250, but we can ignore that last 0.
or 0.250, but we can ignore that last 0.

So 25% equals 0.25 while 0.25% is equal to 0.0025.
So 25% equals 0.25 while 0.25% is equal to 0.0025.

And I want you to maybe sit and think about how small
And I want you to maybe sit and think about how small

of a number 0.25% is.
of a number 0.25% is.

Let's do a couple more and maybe we'll convert going
Let's do a couple more and maybe we'll convert going

the other direction.
the other direction.

Let's say I have the decimal 0.01 and I wanted to convert
Let's say I have the decimal 0.01 and I wanted to convert

that into a percent.
that into a percent.

Well, here we just do it the opposite.
Well, here we just do it the opposite.

We could look at it two ways.
We could look at it two ways.

We could say well, whatever number this is, we multiply it
We could say well, whatever number this is, we multiply it

by 100 and add a percent sign.
by 100 and add a percent sign.

So if you say 0.01 times 100, and then we'll
So if you say 0.01 times 100, and then we'll

add a percent sign.
add a percent sign.

So a.
So a.

0.01 times 100?
0.01 times 100?

Well that's just 1.
Well that's just 1.

You could do the math.
You could do the math.

You add the percent sign.
You add the percent sign.

Well, that equals 1%.
Well, that equals 1%.

Or an even easier way, when we go from a percent to a decimal,
Or an even easier way, when we go from a percent to a decimal,

we move the decimal place over two to the left.
we move the decimal place over two to the left.

So when you go from a decimal to a percent,
So when you go from a decimal to a percent,

we'll do the opposite.
we'll do the opposite.

We move the decimal two to the right.
We move the decimal two to the right.

So if we do that, let me just rewrite it.
So if we do that, let me just rewrite it.

0.01.
0.01.

Just go 1, 2.
Just go 1, 2.

The new decimal place is here.
The new decimal place is here.

If I get rid of that decimals that's 01 decimal 00 whatever.
If I get rid of that decimals that's 01 decimal 00 whatever.

Obviously, this leading 0 means nothing, so that's
Obviously, this leading 0 means nothing, so that's

the same thing as 1.00.
the same thing as 1.00.

Which is the same thing as 1.
Which is the same thing as 1.

And does it make sense that moving the decimal space two to
And does it make sense that moving the decimal space two to

the right-- that's really just the same thing as multiplying
the right-- that's really just the same thing as multiplying

it by 100, right?
it by 100, right?

If I multiply something by 10 it's like moving the decimal
If I multiply something by 10 it's like moving the decimal

space one to the right.
space one to the right.

If I divide something by 10 it's like moving the
If I divide something by 10 it's like moving the

decimal space one to left.
decimal space one to left.

Let's do a couple more while I have time.
Let's do a couple more while I have time.

I think I have three more minutes.
I think I have three more minutes.

Let's say I had 1.25 and I wanted to convert
Let's say I had 1.25 and I wanted to convert

that to a percent.
that to a percent.

Well, the easiest way is just to take-- I'll rewrite it here.
Well, the easiest way is just to take-- I'll rewrite it here.

1.25.
1.25.

Take the decimal point, move it two to the right.
Take the decimal point, move it two to the right.

That's here.
That's here.

And then I'll add a percent.
And then I'll add a percent.

So that equals 125%.
So that equals 125%.

And if you think about it, the way people talk about
And if you think about it, the way people talk about

percent it makes sense.
percent it makes sense.

If I told you that I'm going to pay 1.25 times the
If I told you that I'm going to pay 1.25 times the

price of something.
price of something.

That makes sense that that's also I'm going to pay
That makes sense that that's also I'm going to pay

125% of the price.
125% of the price.

Or if it doesn't make sense hopefully if you do these
Or if it doesn't make sense hopefully if you do these

problems enough it will start to make sense.
problems enough it will start to make sense.

Let's do a couple of more.
Let's do a couple of more.

And you can go back and pause this if you think I'm going too
And you can go back and pause this if you think I'm going too

fast, which I might be doing.
fast, which I might be doing.

Let me think.
Let me think.

If I were to say 0.003 and I want to write
If I were to say 0.003 and I want to write

this as a percent.
this as a percent.

Well, once again, we can move the decimal space
Well, once again, we can move the decimal space

two to the right.
two to the right.

So 1, 2.
So 1, 2.

And that's analogous to multiplying it by 100.
And that's analogous to multiplying it by 100.

So if we multiply the decimal two to the right we get
So if we multiply the decimal two to the right we get

00 decimal point 3.
00 decimal point 3.

And then we add the percent.
And then we add the percent.

At least this first leading 0 doesn't mean anything, so
At least this first leading 0 doesn't mean anything, so

that's the same thing as 0.3%.
that's the same thing as 0.3%.

The important thing to realize is when you're converting from
The important thing to realize is when you're converting from

a percent to a decimal or a decimal to a percent, you're
a percent to a decimal or a decimal to a percent, you're

really just moving where that decimal point is.
really just moving where that decimal point is.

And if you run out of spaces you just have to add or get
And if you run out of spaces you just have to add or get

rid of 0's accordingly.
rid of 0's accordingly.

And the important thing to always have in your mind is,
And the important thing to always have in your mind is,

when I convert from a decimal to a percent, the number in
when I convert from a decimal to a percent, the number in

front of percent signs going to get bigger.
front of percent signs going to get bigger.

And when I go from a percent sign to a decimal, I'm going
And when I go from a percent sign to a decimal, I'm going

to get a smaller number.
to get a smaller number.

If I say 25%, that's the same thing as 0.25.
If I say 25%, that's the same thing as 0.25.

So this is a percent, and this is a decimal.
So this is a percent, and this is a decimal.

So I went from a bigger number, 25, to a smaller number, 0.25.
So I went from a bigger number, 25, to a smaller number, 0.25.

25% is equal to 0.25.
25% is equal to 0.25.

Similarly, if I had a decimal, let's say 0.1.
Similarly, if I had a decimal, let's say 0.1.

When I convert it to a percentage it's going to
When I convert it to a percentage it's going to

be a larger percentage.
be a larger percentage.

So 0.1 is the same thing as 10%.
So 0.1 is the same thing as 10%.

And how did I do that again?
And how did I do that again?

Well I said 0.1, I added an extra 0 because I'm going to
Well I said 0.1, I added an extra 0 because I'm going to

have to move the decimal space over to the right twice.
have to move the decimal space over to the right twice.

So I go 1, 2, and I get a 10.
So I go 1, 2, and I get a 10.

10%.
10%.

Hopefully that answers all your questions for now.
Hopefully that answers all your questions for now.

Have fun.
Have fun.