Converting Fractions to Decimals

Two methods:1. Building a fraction to a base ten number2. Dividing numerator by denominator

Building up the fraction to a base ten number:

2

1

5

5x

10

5.5

25

5 4

4 100

20.20

4

7

25

25*

4

7 100175 1.75

8/3 : Repeating Decimal

83666.2

02

18

20

6

000.83 6.2=

Put a bar over the first number(s) that repeatsAnd drop the rest.

Mixed Fraction to a Mixed Decimal

Whole numbers are to the left of the fraction And to the left of the decimal numbers;

64.3Convert fractional part to decimal byDividing

64.

0100

090

100

60

00.715

15

73

PERCENTSection Understanding Percent

Percent, %, means per hundred.

The percent number is that number compared toa total of 100.

Example: For every $100 invested, you received $6 in return; the interest rate is 6 %

0

10

20

30

40

50

60

70

80

90

100

100

Return

100 100 100 100 100

Return 6 50 75 125

1st Qtr

2nd Qtr

3rd Qtr

4th Qtr

What is the percentage for the following:

386/100

1/100

.07/100

386%

1 %

.07%

WRITE AS A DECIMAL 38%

6%

47%

375%

.38

.06

.47

3.75

WHAT ARE THE RULES TO CHANGE % TO A DECIMAL? EX: 82%

Drop the % symbol 82 Perform the operation the symbol

represents - Divide by 100 - move decimal 2 places .82 What is the clue word? Per - per hundred means divide by 100

WRITING A DECIMAL AS A PERCENT

Move the decimal point two places to the right – (multiply by 100)

0.47 (100%) = 47

47%

Add the % symbol at the end of the number

WHICH WAY TO MOVE DECIMAL?REMEMBER THE ALPHABET

D BEFORE PL BEFORE R

52% D P L R

.005 D P L R

.52

.5%

Remember - 47% is 47 out of every 100. A ratio is a comparison BUT You may not have 47 items.

For every 100 total items, there is 47.

If there were 10 total items, you would have 4.7 items

CHANGING BETWEEN PERCENTS, DECIMALS, AND FRACTIONS

Percent to fraction

Drop the symbol Write the

percent number over 100

reduce

75% 75 75/100

3/4

225 1

__1_

100

Example: 225%

Rewrite % symbol as 1/100

Simplify (reduce fraction) 2 25/100 = 2 1/4

x = 225 100

Example

8

39 % Change to improper fraction

8

75%

Change symbol to fraction

100

1

8

75 Reduce

83

4

1

32

3

Memorize the following equivalents

25%

50%

75%

33 1/3%

66 2/3%

10%

¼½

¾

1/3

2/3

1/10

Fraction to Percent

Can you easily change the denominator to equal 100?

?

?

4

1 %25

100

25

25

25

4

1

?

?

25

34 %136

100

136

4

4

25

34

If denominator cannot be changed easily to 100, find decimal number first.

61.166.

0040

036

040

06

000.166

1 16.67%

Rounded to the nearest Hundredth of a percent

ANOTHER METHOD – FRACTION TO PERCENT:

1008

7 n

Write a proportion

7*100 = 8 n Cross multiply

700 = 8n

n = 87.5%

Divide by 88 8

Changing a fraction to a percent containing a fraction:

Stop the division after two steps

%3291

100

1003

291.12891.

91.0

0008

0012

0020

108

00.111212

11

SOLVING PERCENT PROBLEMS USING AN EQUATION Translating a Percent Problem into an

Equation

What is 5% of 19.00? N = .05 x 19.00 N = .95

Find 0.6% of 400 N = .006 x 400 N = 3.6

35% of what is 60? .35 x N = 60 N = 60 / .35

N = 1714.2

WORDS TO SYMBOLS

“What” becomes n “Is” becomes = Percent numbers become decimals “of” means multiplication

90 is what percent of 20?

90 = p x 20

20

20

20

90 n

4.5 = n

=4.5 * 100%

= 450%

EXAMPLE

Identify the Parts of the Percent Proportion

The base, b, is always multiplied by the rate.In, 16% of 370, 370 is the base.

The amount, a, is always by itself on one side of the equation.In “What percent of 18 is 4.5?”, 4.5 is the amount.

SOLVING % PROBLEMS BY USING PROPORTION A = RB

A, amount

Base = b R= percent Rate

A = b (R)R

b

A b

R

A

When solving for percent,change decimal to percent

100

p

b

A

Cross multiply and then divideBy the variable’s coefficient

100

260

40

a

Ex: Find 260 % of 40

Reduce fraction and cross multiply

A(10)=40( 26)

A = 4 * 26 A = 104

SET UP PROPORTION

100

p

b

A

1004000

160 p 400 p = 16* 100

44

16400

100*16

400

400

P

p

4 %

WHAT PERCENT OF 4000 IS 160?

END BY LORI TSUTSUI

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