Convert Percents, Fractions and Decimals
Fractions to Decimals
Part
Whole
18
20
çthe line means divide
18 ÷ 20
Put the top number in the “house”; it is the dividend
18 ÷ 20 = answer
Dividend ÷ divisor = quotient
__.9
20√18.0
180
0
18 = .9
20
Fractions to Percents
Convert 3 to a percent
5
There are two ways to do this
1. Since percents are based on 100, you can make an equivalent fraction
with a denominator of 100.
3 = ___ 3 x 20 = 60 = 60%
5 100 5 x 20 = 100
_2 x 10 = _20 = 20%
10 x 10 = 100
part = __%
whole 100
2. You cannot always do this, so you may have to make a decimal first.
3
8
__.375
8√3.000
24
60
56
40
40
0
= .375 decimal answer = 37.5% percent answer
D è P
Decimals to Fractions
Millions
,
Hundred thousands
Ten thousands
Thousands
,
hundreds
tens
ones
.
tenths
hundredths
thousandths
ten thousandths
hundred thousandths
We can make a fraction out of EVERY decimal.
Write the number over its place value, then reduce or simplify (must do
this).
.175 number___
place value
_175 ÷ 5 = _35 ÷ 5 = 7
1000 ÷ 5 = 200 ÷ 5 = 40
OR
_175 ÷ 25 = _7
1000 ÷ 25 = 40
.4 write as a fraction
_4 number
10 place value
The 4 is in the tenths place.
Now reduce
_4 ÷ 2 = 2
10 ÷ 2 = 5
.15 =
_15 ÷ 5 = _3
100 ÷ 5 = 20
.65 =
_65 ÷ 5 = 13
100 ÷ 5 = 20
You must reduce or simplify the fraction.
.375 =
_375 ÷ 5 = _75 ÷ 5 = 15 ÷ 5 = 3
1000 ÷ 5 = 200 ÷ 5 = 40 ÷ 5 = 8
.05 =
_05 ÷ 5 = 01 = _1
100 ÷ 5 = 20 = 20
Decimals to Percents
.9
move the decimal two places to the right
.90 fill in the holes with 0’s
.9 = 90%
A trick to remember:
ABCDEFGHIJKLMNOPQRSTUVWXYZ
D to P move rightè
Example:
.44 to percent (%)
D è P
.44
= 44%
Percents to Decimals
Move the decimal two places to the left.
85% = .85
85%
A trick to remember:
P to D move left ç
ABCDEFGHIJKLMNOPQRSTUVWXYZ
Example:
47% to decimal
P ç D
47% = .47
↵↵
OR
3.5% to decimal
P ç D
3.5% = .035
↵↵
fill in holes with zeros
Percents to Fractions
75% to a fraction
_75
100 then reduce or simplify
_75 ÷ 5 = 15 ÷ 5 = 3
100 ÷ 5 = 20 ÷ 5 = 4
_75 = 3
100 = 4
75/100 is called a decimal fraction.
3/4 is called a common fraction.
Example:
62.5% = 5
8
62.5
100
Multiply both top and bottom by 10 because there is 1 digit after
the decimal place. This is to make the top a whole number.
Then simplify/reduce the fraction.
62.5 x 10 = _625 ÷ 25 = 25 ÷ 5 = 5
100 x 10 = 1000 ÷ 25 = 40 ÷ 5 = 8
Example:
150% = 1 ½
150 write down; percent is a whole number; simplify the fraction.
100
150 ÷ 50 = 3 = 1 ½
100 ÷ 50 = 2
Finding the Percent of a Number
Turn the percent into a decimal. P ç D (two places to left)
Multiply the decimal number (from the percent) by the number.
87% x 68 = .87 x 68 = 59.16
Example:
Find 30 percent of 400
30% = .30
.30 x 400 = 120
Repeating Decimal
What if the decimal repeats?
1
3
Part
Whole
1
3
çthe line means divide
1÷3
Put the top number in the “house”; it is the dividend
1
÷ 3
= answer
Dividend ÷ divisor = quotient
_.3333
3√1.0000
-9 ê| |
10 | |
-9ê|
10
- 9ê
10
-9
1
You write it with a line over the digits that repeat.
1 = _
3 .33
This is called a repeating decimal.
Terminating Decimal
3
5
_.6
5√3.0
-30
0
3 = .6
5
This decimal stops. It is called a terminating decimal.