Rational Number (Fraction, Decimal, Percent) Conversions
From a fraction to a decimal
Option 1: Divide (Top In, Bottom Out)
1
**Convert
into a decimal.
3
0.333
3 1.000
-9
10
-9
10
Since the 3 repeats, it is written as 0.33 .
Option 2: Write an equivalent fraction
with a denominator of 10, 100, or 1,000.
Read it and use place value to write the
decimal number.
**Convert
4
into a decimal.
5
4
8
, which is read as “eight-tenths.”

5 10
From a decimal to a fraction
Read the decimal number the “proper”
way. Write the fraction using place value.
Then simplify/reduce.
**Convert 0.3 into a fraction.
The “proper” way to say 0.3 is “threetenths,” since the last digit is in the tenths
place. This means to write 3 over 10.
3
Therefore, 0.3 =
.
10
**Convert 0.04 into a fraction.
The “proper” way to say 0.04 is “fourhundredths,” since the last digit is in the
hundredths place. This means to write 4
over 100.
4
Therefore, 0.04 =
, which can be
100
4
1
simplified by to equal
.
4
25
Thus, the last digit should be written in the
tenths place, which is written as 0.8.
From a decimal to a percent
Move the decimal point two places to the
right (which is the same as multiplying by
100).
**Convert 0.1 into a percent.
From a percent to a decimal
Move the decimal point two places to the
left (which is the same as dividing by 100).
**Convert 9% into a decimal.
Move the decimal point twice to the right,
and fill in any empty places with zeroes.
Therefore, 0.1 = 10%.
Move the decimal point, which is behind
the 9, twice to the left. Fill in any empty
places with zeroes. Be sure to remove the
percent sign. Therefore, 9% = 0.09.
**Convert 3 into a percent.
**Convert 0.79% into a decimal.
The decimal point is behind the 3, since it
Move the decimal point twice to the left.
is a whole number (think of $3.00). Move it Fill in any empty places with zeroes.
twice to the right. Therefore, 3 = 300%.
Therefore, 0.79% = 0.0079.
From a fraction to a percent
Option 1: Write an equivalent fraction
with a denominator of 100, since a percent
is out of 100. The numerator is the percent
amount.
**Convert
4
into a percent.
5
4
80
. The numerator (top number)

5 100
4
becomes the percent, so = 80%.
5
**Convert
3
into a percent.
4
3
75
. The numerator (top number)

4 100
3
becomes the percent, so = 75%.
4
From a percent to a fraction
Write the percent amount over 100 and
simplify.
** Convert 35% into a fraction.
Write 35 over 100 and simplify.
35 5
7
7
÷ 
. Thus, 35% =
.
100 5 20
20
Note: If there is a decimal point, move the
decimal in the numerator and denominator
to the right the same number of times until
the decimal is at the end of the numerator.
Then simplify.
**Convert 12.5% into a fraction.
Write 12.5 over 100.
Option 2: Convert the fraction to a
decimal (see “From a fraction to a
decimal”). Then convert it to a percent
(see “From a decimal to a percent”).
12.5
100
The fraction has a decimal in it, so move
the decimal to the right in both the
numerator and the denominator until it is
at the end of the numerator. Fill in any
empty places with zeroes.
12.5
125
125

can be simplified by
to
100 1000
125
1
1
become . Thus, 12.5% = .
8
8