>> Hi. This is Julie Harland,
and I'm your math gal.
Please visit my website
at yourmathgal.com
where you can search for any
of my videos,
organized by topic.
This is part one of decimals.
In this video,
we go over the beginning
of decimal notation
and place value,
and we do the
following problems.
We're going to be working
with decimals now,
so we're going to start off
with decimal notation
and place value.
So you already know
about whole number
place value.
Remember you had the one,
the 10, the 100,
1,000ths place, et cetera.
Notice that to get the next
number to the right,
you would just multiply by 10.
So if you had 1,
the next place value,
multiply by 10.
Then i fyou multiply the 10
times 10, you're going
to get 100.
And if you multiply
that by 10, 100 times 10,
you'll get 1,000.
So decimal notation is a base
10 system.
In other words, you multiply
by 10 to get the next place
value to the left.
Now, let's go the other way.
What if you were
over here at 1,000?
How would I get the next place
value to the right?
You would --
how would I get
from 1,000 to 100?
You end up dividing 1,000
by 10 to get to 100.
And you divide 100 by 10,
you'll get 10.
And if you divide 10 by 10,
you'll get to one.
So if we kept going,
what would this next place
value be over here?
If I take 1 and divide it
by 10, one way of writing 1
by 10 is a fraction.
1 divided by 10.
This is actually the
one-tenth place.
When you're working
with decimals,
it's a special way
of writing certain kinds
of fractions.
So we have
to really already understand
fractions for decimals
to really make sense.
Alright, so let's say I wanted
to get the next place
value over.
I would divide that by 10.
That's a little bit tricky
writing 1/10 divided by 10.
But let's see.
How could I do that?
1/10 divided
by 10 is 1/10 times 1-over-10,
which is 1/100.
So this next place value is
going to be 1-over-100.
And the next one's going
to be 1-over-1,000.
Same reasoning.
And the next one is going
to be 1-over-10,000,
et cetera.
Alright, if we have a number
like 45.3,
basically there's a whole
number part --
that's the part before the
decimal, which would be 45 --
and then there's this number
after the decimal.
And there's a 3 after it.
So first of all,
notice the place values again
for the parts
after the decimal point.
Notice the first one is 1/10,
the second place is 1/100,
the third place is 1/1,000.
One easy way
to remember these is,
it's a fraction,
and if it's one place
after the decimal point,
there's one zero
in the denominator.
10, right,
is in the denominator.
Two places
after the decimal point,
there's 1 with two zeros
in the denominator.
Three places
after the decimal point,
there's a 1 with three zeros
after the decimal point.
So we've got this example,
45.3.
That's how a lot
of us read this number,
but actually,
the whole number part is 45,
and the fractional part,
what we could say is, "Well,
if that 3,
since it's one place
after their decimal point --
see, if I were going
to write it up here --
3 is in the 10th place,
it's really just 45 and 3/10.
Before doing some more
like this, let's just work
on some problems
that only have digits
after their decimal point.
So they're going to be numbers
between zero and one.
So here are a few problems
to get started.
We want to write the number
as a fraction
and then write it in words.
So all of these only have one
digit that's not a zero.
So that's what really is
important here.
So what is this number here?
0.04? Well, we've got a 4.
And what place value is
that in?
It's 4-something.
Well, it's two places
after the decimal point.
So it's 4/100.
Now, I know
that can be reduced,
but I'm not going to worry
about reducing it right now.
Let's write this in words.
How would you say this?
You would say four-hundredths.
Oops. Now, you don't want
to say four-hundreds.
You have to remember
to put TH: four-hundredths.
Okay? Four-hundredths,
telling you it's less
than one.
Okay, let's do the next one.
Try it on your own.
See if you can write it
as a fraction.
And then how would you write
it in words?
Okay. So we've only got one
digit: the 3.
And let's see.
It's going to be a 1
with how many zeros after it?
Well, the 3 is
in the third place
after the decimal.
So let's put three zeros
after the 1.
What number is that?
3/1,000. So I would just
say three-thousandths.
Alright. How
about this next one?
Only have a 7.
And there's only one place
after the decimal point,
right?
So it's over 10, 7/10.
That's all you write:
seven-tenths.
So notice on all
of these you always have
to put the T-H-S after it:
tenths, hundredths,
thousandths, et cetera.
Don't confuse that with ten,
hundred and a thousand.
Now, when you have a number
in front of the decimal point,
that will be the whole
number part.
And then there's the
decimal point.
And then there will be a
decimal or fractional part
after that.
That's the one
between zero and one.
In the middle
where the decimal point is,
we're always going to read
that as the word "and."
So let's see how we would
write this.
We want to write this number
-- 102.04 --
as a mixed number
and in words.
Alright. So what we do is we
separate out the whole
number part.
That's before the decimal.
Well, that's 102.
So we'd write,
"One hundred two."
If you remember
when we did place values
of whole numbers,
we don't use the word "and,"
because this is
when we finally get
to use the word "and."
If there's a whole number part
and decimal part.
And here it comes.
And. And that breaks
up the decimal part.
Now we'll look at the part
after the decimal point,
right here, okay?
And the number is 4.
That's all we see, right?
And we have to decide where...
[ Silence ]
Alright, let's do
this problem.
Write 102.04 as a mixed number
without reducing the
fractional part, and in words.
So let's try it
as a mixed number.
Well, we have the part before
the decimal point.
And we have the part
after the decimal point.
So the part before is just
that number itself: 102.
So you simply write that out.
And what about the
part afterwards?
Well, .04.
So we've got a 4,
and we just have
to decide what the fractional
part is.
It's two places
after the decimal, so it's a 1
with two zeros.
So that's how I write this
as a mixed number.
And yes, I know it can
be reduced.
Now, how are we going to write
that in words?
Well, you can see it right
here: "one hundred two" is the
whole part, right?
[ Silence ]
But here's the point.
There was an "and"
where that decimal point is.
That's where we put "and."
When we did place values
with whole numbers,
we did not use the word "and,"
because it's used
when you have a mixed number
like this.
The whole part
and a fractional part
or a decimal part.
So we have
"one hundred two and" --
notice from this fraction you
can see it's 4/100, okay?
But you should also be able
to do that without writing the
fraction part first.
You look at this first
and say, "Well,
4 is in the hundredths place,"
so you could write,
"and four-hundredths."
So let's try another one
like that.
Alright. So try this one
on your own.
You want to write it
as a mixed number,
and you also want
to write it in words.
Okay. So remember the decimal
point is --
that separates the whole
number part
from the fractional part.
So the whole number part
is 20.
This time,
I'm going to write it
in words first.
Okay? So 20.
Then we see a decimal point,
right?
Remember what that means?
"And." And then we have the
part after the 20,
which is 7, right?
And then I have
to decide what place value
that's in.
Well, it's one, two,
three places
after the decimal point.
So think about 1
with three zeros.
What would that stand for?
That would stand for 1,000.
So this will be thousandths.
[ Silence ]
Now, let's write
that as a mixed number.
Okay, the whole part is 20.
So you write "Twenty."
And then after the decimal
point is 7,
so that's the numerator.
And then you would say, "Oh,
there's three places
after the decimal point,"
so it's 1 with three zeros
after it.
Twenty and seven-thousandths.
So this number, 20.007,
means twenty
and seven-thousandths.
It's actually best
to say it this way,
although a lot of us are lazy
and we say, "20.007."
But if you read it this way,
twenty and seven-thousandths,
it sort of drives home
that this is really just a
fraction, right?
This .007.
[ Silence ]
Please visit my website
at yourmathgal.com
where you can view all
of my videos,
which are organized by topic.