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Decimals
a) Decimal Notation
- a finite decimal part = the decimal number does not go on forever.

example: 0.56 = 56/100
- an infinite decimal part = three points are added to show that the decimal number goes on forever.

example: 22/7 = 3.14159…
o place a horizontal line called vinculum over numbers that repeat in an infinite decimal
part.
 example: 1/9 = 0.11111111111… or 0. 1
b) Decimal Fraction
- a decimal fraction is a fraction whose denominator is a power of 10.
 example: 5/1, 3/10, 23/100, 17/1000, 23 891/10 000
c) Place values

example: 0.3, 0.017 and 2.3891
3
0
3
1
8
7
9
0.0000
1
1/100
00
1
0.000001
1/100000
Millionths
.
.
.
0.001
1/100
0
Hundred
Thousandths
0
0
2
0.01
1/100
Ten Thousandths
.
Thousandths
1
0.1
1/10
Hundredths
Tenths
.
10
Ones
10
0
Tens
Thousands
…
100
0
Hundreds
…
0.0000001
1/1000000
…
d) Order
To order numbers expressed in decimal notation, first, compare the integer part. If the integer part is
the same for each number, the compare the decimal part, place by place, from biggest to smallest. The
number that has the biggest digit first is the larger number.
Example:
a) 9.76 < 9.81
b) 5.625 > 5.6219
c) 6.785 < 6.793 < 8.13 < 8.2 < 8.246
e) Converting fractions to decimals
1/4
1.
2.
3.
4.
5.
6.
7.
8.
9.
convert fraction to x/100 or x/10x
1/4 (multiply top and bottom by 250) = 250/1000
look at how many zeroes there are in the denominator  3
start from the right side of the numerator number and move to the left as many times as you
have zeroes and place a decimal point where you stop.
250
if nothing precedes the decimal point, put a zero to the left of the decimal point.
250
if there is a space between the decimal point and your numerator, put zeroes to the right of the
decimal point.
example: 1/100 = 0.01
f) Different method of converting from fraction to decimal (other than the way we learned
previously):
o
divide the numerator by the denominator.
 Example: Convert 2/5 to a decimal
 Divide 2 by 5 = 2 ÷ 5 = 0.4
 Answer = 2/5 = 0.4
g) percentages and Decimals:
-
1. To convert from percent to decimal divide by 100 and remove the % sign.
o To divide by 100 move the decimal point 2 places to the left.
-
2. To convert from decimal to percentage multiply by 199 and add the % sign.
o To multiply by 100 move the decimal point 2 places to the right.
h) percentages and Fractions:
-
1. To convert fractions to percentages divide the numerator by the denominator and multiply
the result by 100, and add the "%" sign.
Example: Convert 3/8 to a percentage
o
o
o
-
First divide 3 by 8: 3 ÷ 8 = 0.375,
Then multiply by 100: 0.375 x 100 = 37.5
Add the "%" sign: 37.5%
 Answer: 3/8 = 37.5%
2. To convert percentages to fractions first convert to a decimal (divide by 100), then use the
steps for converting decimal to fractions.
Example: convert 80% to a fraction
o
o
o
o
Convert 80% to a decimal (divide by 100 and remove the % sign) = 0.80
Put the decimal over 1 = 0.8/1
Then multiply top and bottom by 10 for every number after the decimal point (10 for 1
number, 100 for 2 numbers, etc) = 0.8 has one number after the decimal point so
multiply by 10.
 Example: 0.88/1 would be multiplied by 100 because there are two numbers
after the decimal point = 88/100
Reduce or simplify if needed.