>> Welcome to an introduction to decimal notation.
The goals of this video are to read a number in decimal notation.
Compare and order numbers in decimal notation.
And also to round numbers in decimal notation.
Decimal notation is used to write numbers according to place value in base ten.
A decimal point is used to separate whole numbers from numbers that are less than 1.
And we see decimals all the time in our real life.
For example, if it costs 2 dollars and 89 cents per gallon of gas.
The 2 represents 2 whole dollars and the 89 to the right
of the decimal point represents 89 hundredths of 1 dollar.
If the runner finished the race in 10 point 3 seconds.
That means it took the runner 10 whole seconds and 3 tenths of a second to finish.
Since the digits to the right of the decimal represent a number less than 1.
We can also represent decimals as fractions.
Let's go and take a look at that.
You want to be able to read each of these numbers
and then write them using fractional notation.
So for 6 point 3, we would read this 6 and for the decimal point 3 tenths.
So 6 point 3 equals 6 and 3 tenths.
This is a mixed number.
If we wanted to write this as a fraction we could convert this to an improper fraction,
10 times 6 plus 3 would be 63 tenths.
For number 2, we would have 52 and 12 hundredths.
If we convert this to an improper fraction 100 times 52 that would be 5200 plus 12.
So 5212 over 1000.
Now this does simplify but we're going to leave it in this form
because it does show the place value.
And this is often called a decimal fraction.
In our last example number 3, we would have 1 and 125 thousandths.
So here's the decimal as a mixed number.
And then as a fraction it would be 1125 thousandths.
Okay let's go ahead and take a look at comparing numbers
in decimal notation using greater than, less, than, or equal.
One thing we can do when we have a decimal point
in a number is add zeros to the right of the number.
Because if I add a zero here, I'd be adding zero thousandths
and therefore it would not change the value of that number.
Now if we wanted to we could write this as 5 and 219 thousandths.
And this would be 5 and 220 thousandths.
When it's written in fraction form with a common denominator it's pretty easy to tell
if this number here is smaller than the second.
Therefore we would say that 5 point 219 is less than 5 point 22.
So really what we're doing when we add extra zeros
to the right is we're obtaining a common denominator in fraction form.
And I think that's a nice way to do a comparison.
On number 2 this has four digits to the right of the decimal point,
so we're going to add a zero here.
When we do that we can easily see that these are now the same number and therefore equal.
Another way to compare when you have just two numbers would be
to just compare each place value to determine which one is larger or smaller.
So what I mean by that is, notice these both have a whole number of 18 if you look
at the tenths place this has 9 tenths this only has 8 tenths.
So 18 point 9 would be larger than this second, therefore it's greater than the second.
But I actually prefer to add extra zeros to the right so they have the same number
of digits to the right of the decimal.
And that comes in very handy when we have a list of numbers like we see here.
We want to order them from least to greatest.
So I'm going to go ahead and rewrite these on the right side of the screen.
Line up the decimal point and the place values and then do our comparison.
So if you line this up vertically and add zeros to the right so they have the same number
of digits to the right of the decimal.
We would have to add one zero here.
One zero here.
Two here and two here.
Remember when comparing numbers the smallest numbers occur to the left on the number line.
And the largest occur to the right on the number line.
So in this list I noticed there are two negative numbers.
And negative 5 point 8 would be to the left of negative 3 point 04.
So negative 5 point 8 would be the smallest or the least number
from the list followed by negative 3 point 04.
Notice when you rewrite your list, you should give them back in the same form they were given.
So we're not going to include the extra zeros.
Okay these 2 numbers are out.
Now because they have the same number of digits.
Now if we compare the tenths place value these both have 1 tenths but this has zero tenths.
Therefore this would be the next number in the list.
We have two numbers left and we have to determine which one would be smaller.
If you look at the hundredths place value, this has zero hundredths this has 1.
So 3 point 1 is smaller than 3 point 11.
Let's go ahead and try one more.
Let's go ahead and rewrite these vertically and line up the decimal point.
This number has four digits to the right of the decimal point.
So let's go ahead and add some extra zeros here.
That one needs two.
This one needs one.
And this one needs one.
They all have 12 to the left of the decimal.
They all have zero in the tenths.
Next these two have zeros in the hundredths.
So these two are smaller than the remaining two.
This one has an 8 in the thousandths, this one has 9.
So 12 point 008 would be the smallest.
Followed by 12 point 0098.
Okay those two are out.
Look at the thousandths place.
This has 1 thousandths, this doesn't have any.
Therefore 12 point 01 would come next.
Followed by 12 point 011.
Okay, let's go ahead and finish by talking about rounding.
Rounding decimals is very similar to rounding whole numbers.
Step 1, is to identify the round off digit.
Step 2, if the digit to the right of the round off digit is less than 5 we round down.
So we do not change the round off digit.
If it's 5 or more, we round up by increasing the round off digit by 1.
In either case we drop all digits to the right of the round off place digit.
So if we want to round this to the hundredths.
Step 1, the 2 is in the hundredths place value.
And the digit to the right or this 5 here is the decision maker.
Because it's a 5 we round up so we change the 2 to a 3, 12 point 13.
Now it's important that we do not include any extra zeros to the right
because this tells the reader we rounded to the hundredths place value.
If we add an extra zero here, it would be assumed
that we rounded to a different place value.
On number 2, the 1 is the tenths and the 2 is the decision maker.
The 2 tells us to round down so we leave it as a 1, and we have 5 point 1 or 5 and 1 tenth.
And number 3, the ten-thousandths.
We have the tenths, hundredths, thousandths, and ten-thousandths would be here.
The 7 is our decision maker.
So we're going to round up so we change the 2 to a 3, 16 point 0983 and then we stop.
Okay that'll do it for this video.
Thank you for watching
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