Let's get started and learn how to convert
percentages to decimals.
And if we have time maybe we'll also learn how to convert
decimals into percentages.
So let's get started with what I think is a problem you
probably already know how to do.
If I said I have 50%.
I don't know if I wanted to write that thick,
but we'll go with it.
Actually, let me change it to a thinner one.
And I want to turn that into a decimal.
Well you probably already have a sense of what
decimal represents 50%.
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
say half as a decimal?
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
convert this 50% to 0.5?
Well, it turns out it's pretty straightforward.
All you do is you say-- whatever percentage it is,
that's the same thing as the number over 100.
And 50/100 is the same thing as 5/10 or 0.5.
Now even a simpler way of converting percentage to
decimals and, I think, you're going to realize converting a
percentage to a decimal or the other way around, you can
pretty much do it in your head.
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%.
If I want to convert that 50.0% into a decimal, all I do is I
get rid of the percent sign.
So I'll do it here.
50.0%.
I get rid of the percent sign and I take the decimal point
and I move it over two spaces to the left.
So I say 1, 2.
So this is where the new decimal is.
So this equals we could say 0.500.
So 50.0% is equal to 0.500.
And of course, these last two 0's really don't mean anything
for our purposes, so we'll get rid of them.
So that's the same thing as 0.5 or just 0.5.
50% equals 0.5.
So you're probably saying, well, sure.
That looks easy, but what if the problem gets
a little harder?
50% I could have done in my head.
So let's try some, I would say, slightly harder problems.
If I were to tell you that-- let's say 16.32%.
Well, let's just do it the way I just showed you.
I'll rewrite it down here.
16.32%.
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.
So 1, 2.
This is the new place for the decimal.
That decimal goes away.
So it's 0.1632 is equal to 16.32%.
I think you might be getting the idea now.
Let me do another one in green.
Let's say I had-- and this one actually confuses
a lot of people.
Let's say I had 0.25%.
So the important thing to remember is, I'll rewrite here.
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
second why I wrote that leading 0 there even though it doesn't
seem to add much to it.
00.25%.
Well, what's the system I just showed you?
You get rid of the percent sign and you move the
decimal over 1, 2 spaces.
So that equals 0.0025.
So 0.25% is equal to 0.0025.
And you could put a leading 0 here if you want.
Actually, I should probably tell you to always do that
because it makes it easier to read.
So 0.25% is equal to 0.0025.
And I want to just contrast that with 25%.
25%, what do you think that equals?
Well.
you do the same thing that we've been doing.
You get rid of the percent sign and you move the decimal space.
In this case-- actually, let me leave that there.
I'll just rewrite it here.
25%.
And you're probably saying, where is the decimal in this?
Well, the decimal is after the number because that 25% is
the same thing as 25.0%.
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,
or 0.250, but we can ignore that last 0.
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
of a number 0.25% is.
Let's do a couple more and maybe we'll convert going
the other direction.
Let's say I have the decimal 0.01 and I wanted to convert
that into a percent.
Well, here we just do it the opposite.
We could look at it two ways.
We could say well, whatever number this is, we multiply it
by 100 and add a percent sign.
So if you say 0.01 times 100, and then we'll
add a percent sign.
So a.
0.01 times 100?
Well that's just 1.
You could do the math.
You add the percent sign.
Well, that equals 1%.
Or an even easier way, when we go from a percent to a decimal,
we move the decimal place over two to the left.
So when you go from a decimal to a percent,
we'll do the opposite.
We move the decimal two to the right.
So if we do that, let me just rewrite it.
0.01.
Just go 1, 2.
The new decimal place is here.
If I get rid of that decimals that's 01 decimal 00 whatever.
Obviously, this leading 0 means nothing, so that's
the same thing as 1.00.
Which is the same thing as 1.
And does it make sense that moving the decimal space two to
the right-- that's really just the same thing as multiplying
it by 100, right?
If I multiply something by 10 it's like moving the decimal
space one to the right.
If I divide something by 10 it's like moving the
decimal space one to left.
Let's do a couple more while I have time.
I think I have three more minutes.
Let's say I had 1.25 and I wanted to convert
that to a percent.
Well, the easiest way is just to take-- I'll rewrite it here.
1.25.
Take the decimal point, move it two to the right.
That's here.
And then I'll add a percent.
So that equals 125%.
And if you think about it, the way people talk about
percent it makes sense.
If I told you that I'm going to pay 1.25 times the
price of something.
That makes sense that that's also I'm going to pay
125% of the price.
Or if it doesn't make sense hopefully if you do these
problems enough it will start to make sense.
Let's do a couple of more.
And you can go back and pause this if you think I'm going too
fast, which I might be doing.
Let me think.
If I were to say 0.003 and I want to write
this as a percent.
Well, once again, we can move the decimal space
two to the right.
So 1, 2.
And that's analogous to multiplying it by 100.
So if we multiply the decimal two to the right we get
00 decimal point 3.
And then we add the percent.
At least this first leading 0 doesn't mean anything, so
that's the same thing as 0.3%.
The important thing to realize is when you're converting from
a percent to a decimal or a decimal to a percent, you're
really just moving where that decimal point is.
And if you run out of spaces you just have to add or get
rid of 0's accordingly.
And the important thing to always have in your mind is,
when I convert from a decimal to a percent, the number in
front of percent signs going to get bigger.
And when I go from a percent sign to a decimal, I'm going
to get a smaller number.
If I say 25%, that's the same thing as 0.25.
So this is a percent, and this is a decimal.
So I went from a bigger number, 25, to a smaller number, 0.25.
25% is equal to 0.25.
Similarly, if I had a decimal, let's say 0.1.
When I convert it to a percentage it's going to
be a larger percentage.
So 0.1 is the same thing as 10%.
And how did I do that again?
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.
So I go 1, 2, and I get a 10.
10%.
Hopefully that answers all your questions for now.
Have fun.