|
Decimals are also
use to name numbers between whole numbers.
Decimals are the
same as Fractions with denominators that are multiples of
10.
5 tenths = 5/10 =
0.5
5 hundredths = 5/100
= 0.05
5 thousandths =
5/1,000 = 0.005
125 thousandths =
125/1,000 = 0.125
|
Place positions of
decimals |
|
1000s
thousands |
100s
hundreds |
10s
tens |
1s
ones |
. |
0.1s
tenths |
0.01s
hundredths |
0.001s
thousandths |
|
|
2 |
4 |
6 |
. |
8 |
5 |
2 |
|
|
|
|
|
|
|
|
|
The first position to the right of the
decimal point represents tenths – which is one divided into
10 parts.
The second position
to the right of the decimal point represents hundredths –
which is one divided into 100 parts.
The third position
is thousandths – which is one divided into 1,000 parts.
The number on the
third line is:
Words – two hundred
forty six point eight five two
Decimal notation:
246.852
Fraction notation:
246 852/1000, or 246 and 852 thousandths
A special use for
decimals is how we write money numbers. We count money in
dollars and cents. We use the symbol ‘$’ in front of the
money decimal number.
We write the
dollars as whole numbers, and the cents as a decimal number.
The decimal point comes after the whole number. The cents
are really hundredths of a dollar.
If a cheeseburger
costs 3 dollars and 99 cents, we would write:
$ 3.99
This means 3 dollars
and 99 hundredths of another dollar.
|
Comparing Decimal
Numbers |
Here are some
examples of decimal numbers that are equal:
0.4 = 0.40 = 0.400
( 4 tenths = 40 hundredths = 400 thousandths)
0.25 = 0.250 =
0.2500 ( 25 hundredths = 250 thousandths = 2500
ten-thousandths)
When comparing
decimal numbers, it helps to add zeroes to the right of the
last digit so that the decimal numbers you are comparing
have the same number of digits to the right of the decimal
point.
For example,
compare 0.4 with 0.060
First change the 0.4
to 0.400
Now we can compare
0.400 and 0.060
0.400 > 0.060 since
400 is > 60
Compare 0.205 with
0. 21
First change 0.21 to
0.210
Now we can see that
0.205 < 0.210 since 205 < 210
|
Adding and
Subtracting Decimals |
You add and subtract
decimal numbers the same way you add and subtract whole
numbers with one additional rule:
|
Always line up the decimal points of the numbers so
that the decimal points are in the same column. This
ensures that you are adding numbers with the same
place value. Sometimes, it is helpful to add zeroes
to the end of a number so that all numbers have the
same number of digits to the right of the decimal
point. |
Example: Add 3.4 +
28.76 + 0.001
|
|
3 |
. |
4 |
0 |
0 |
|
2 |
8 |
. |
7 |
6 |
0 |
|
|
0 |
. |
0 |
0 |
1 |
|
3 |
2 |
. |
1 |
6 |
1 |
Remember: You need
to write your numbers neatly!!!
|
Adding and
Subtracting Money |
You add or subtract
money numbers the same way you add and subtract decimals.
Make sure you line up the decimal points neatly.
$ 235.56
-$ 55.45
$ 180.11
0.75 is read as 75 hundredths. So if 1 is
divided into 100 parts, 0.75 means 75 of those one hundredth
parts.
0.60 is read as 60
hundredths. Again, if one is divided into 100 parts, 0.60
means 60 of those hundredth parts.
Percent means per
hundred or out of a hundred. 75% means 75 out of 100.
60% means 60 out of
100.
¾ = 0.75 = 75/100 =
75%
3/5 = 0.60 = 60/100
= 60%
½ = 0.50 = 50/100 =
50%
0.93 = 93/100 = 93% |
