Introduction to Decimals Part I

Uploaded by MuchoMath on 17.03.2009

>> Professor Perez: Hey!
This is Professor Perez from Saddleback College.
Today we're going to an introduction to decimals.
Now, this will be a two part presentation.
Now of course, we can't get started without our student of the semester, and that's Charlie.
He better be ready to go!
Hey, Charlie, you ready to go?
>> Charlie: Yeah!
>> Professor Perez: We're doing decimals today, an introduction.
Here we go, right there.
Okay, Charlie, on the first day of class we discussed digits and place value.
There was our digits and we put this number up.
And we defined a pattern that exists when you look at place value, now here it is again.
Ones, tens, hundreds.
One thousand, ten thousands, hundred thousands.
One million, ten millions, hundred millions.
One billions, ten billions, hundred billions, and we bring it home with one trillions.
Now, you asked me a question on that first day, what about the decimal?
Well, here we go.
If you remember, it's said that everything appears to mirror off that ones place.
Watch. The pattern will exist, but it goes in reverse, just like this.
Ones, tenths, hundredths.
One thousandths, ten thousandths, hundred thousandths.
One millionths, ten millionths, hundred millionths.
One billionths, ten billionths, hundred billionths.
So, remember, we're going to look at place values
of decimal numbers so we can read the correctly.
So, here we go, Charlie.
Right there.
0.07 Well, that's how most people say it.
But how do we say this as a word statement?
Well, first to find the place value of the 7 digit.
Ones, tenths, hundredths.
There we go.
So our 7 is in the hundredths place
and therefore how many hundredths do we have, Charlie?
>> Charlie: 7.
>> Professor Perez: That's right.
Now, how do we write this as a fraction?
Well, it's 7 over 100.
There you go.
And there's a decimal written as a fraction and is said, 7 hundredths.
Let's do another one.
Here we go, Charlie.
0.18 If we're going to read that correctly as a word statement, let's define the place value.
Ones, tenths, hundredths.
Right? And the 8 is in the hundredths place.
How many hundredths do we have, Charlie?
>> Charlie: 18.
>> Professor Perez: 18.
We have 18 hundredths.
And as a fraction, it's 18 over 100.
Now, you could reduce that fraction to 9 over 50 if you'd like, but right now,
we're just trying to write the decimals as a fraction whose denominator is a power of 10,
right, because decimals are fractions whose denominators are powers of 10.
100 is 10 squared, we'll talk more about that later, too.
Okay, Charlie, we're having so much fun, let's do another one.
All right, don't get scared.
Now, how do you read this one?
You don't want to say point oh-oh-oh-oh eight, right?
You've got to find the place value, so, here we go.
Ones, tenths, hundredths.
One thousandths, ten thousandths, hundred thousandths.
One millionths.
Don't get scared, Charlie.
Now, the 8 is in the one millionths, so how many one millionths do we have, Charlie?
>> Charlie: 8.
>> Professor Perez: Very nice there.
And now that you can say it properly, as a word statement, we can easily write the fraction.
It's 8 over 1,000,000.
There we go.
Let's do another one now.
Here we go.
0.00201 Well what number's that?
Let's start by finding the place value of our furthest digit to the right.
Ones, tenths, hundredths.
One thousandths, ten thousandths, hundred thousandths.
There we go.
And so we see that 1 is in the hundred thousandths.
How many hundred thousandths do we have, Charlie?
>> Charlie: 201.
>> Professor Perez: Two hundred and one hundred thousandths.
And so to write this as a fraction, notice we just put 201 over 100,000 There you go.
And of course, if you have a calculator, and you take 201 and divide
by 100,000 you're obviously going to get that 0.00201 because that's 201 hundred thousandths.
All right, Charlie, let's do another one.
Now, 4.023 Charlie.
This is actually a mixed number.
It's a whole number with a decimal.
So, let's define our place values.
The 4's in the ones, and then we have the tenths, hundredths, one thousandths.
And so notice, that 3 is in the one thousandths Charlie.
But first, we have a whole number that's a 4, so we'll put that down.
4 and now, here's where we're using the word and because we have a mixed number.
We have 4 and what, Charlie?
>> Charlie: 23 one thousandths.
>> Professor Perez: 23 one thousandths.
Now, let's write the number as a mixed number.
Watch. 4 and 23 one thousandths.
There is the mixed number notation for that decimal up there.
Phew! Let's do one more, Charlie!
3.0250 Notice, there's a 0 at the end of the decimal.
Well, some people have asked me, do we need to put that 0 there?
Well, not putting a 0 there or removing it really,
is not going to change the actual value of the number.
But we're going to get into something called significant figures.
This number right here is given to the nearest ten thousandths.
So you were asked to give a decimal representation
of some number rounded to the nearest ten thousandths.
So, we're going to translate just as the decimal number is given.
You can talk more about significant figures with your facilitator, your tutor,
your teacher, or your parents, right?
Okay. So, here we go, Charlie, we have the Ones, tenths, hundredths.
One thousandths, ten thousandths.
So that 0 is in the ten thousandths place, so, we have a whole number Charlie, what is it?
>> Charlie: 3.
>> Professor Perez: So we have 3 and what, Charlie?
>> Charlie: 250.
>> Professor Perez: 250 ten thousandths.
Very nice.
Now let's write this in its mixed number notation.
3 and 250 over 10,000.
Very nice there Charlie!
Phew, that was a good warm up for part two!
Anyway, we'll see you again soon!