Fraction to Decimal.doc

7/15/2019 Fraction to Decimal.doc

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Fraction to Decimal

Relationship between Percentage, Fractions andDecimals.

A. Expressing percentages as the numbers of parts in every 100.

Percentage is a fraction with 100 as the denominator.

Example, 9% = 9/100 and 17/100 = 17%

B. Changing fractions and decimals into percentages and vice versa.

Convert Fractions to Percents

Divide the top of the fraction by the bottom, multiply by 100 and add a "%" sign.

The simplest method is to use a calculator:

Steps:

• Divide the top of the fraction by the bottom,

• Then multiply the result by 100 and read off the answer !

Example: What is 5/8 as a percent?

Get your calculator and type in "5 ÷ 8 =", the calculator should show 0.625, then multiply by

100 and your answer is: 62.5% (remember to put the "%" so people know it is "per 100")

Of course you can do the division in your head or on paper if you don't have a calculator!

Another Method

Percent means "per 100", so try to change the fraction to

?

form

100

Follow these steps:

Step 1: Find a number you can multiply the bottom of the fraction by to get 100.

Step 2: Multiply both top and bottom of the fraction by that number.

Step 3. Then write down just the top number with the "%" sign.

http://www.mathsisfun.com/scientific-calculator.html



Fraction to Decimal

Example 1: Express3/4 as a Percent

Step 1: We can multiply 4 by 25 to become 100

Step 2: Multiply top and bottom by 25:

×25

3

=

75

4 100

×25

Step 3: Write down 75 with the percent sign:

Answer = 75%

Example 2: Express3/16 as a Percent

Step 1: We have to multiply 16 by 6.25 to become 100Step 2: Multiply top and bottom by 6.25:

×6.25

3

=

18.75

1

6 100

×6.25



Fraction to Decimal

Step 3: Write down 18.75 with the percentage sign:

Answer = 18.75%

Yet Another Method

Because a percent is actually a ratio (parts per 100) we can also use Proportions to do the

conversion.

First, put what you know into this form:

Top of Fraction

=

Percent

Bottom of Fraction 100

Then solve using "multiply across the known corners, divide by the third number":

Example: convert 3/16 to percent

Fill in what you know:

3

=

Percen

t

16 100

Multiply across the known corners, then divide by the third number. The "known corners" aretop left and bottom right:

Percent = (3 × 100) / 16 = 300 / 16 = 18.75%Answer: 3/16 is 18.75% (just like the previous example!)

C. Convert Fractions to Decimals

The simplest method is to use a calculator.

Just divide the top of the fraction by the bottom, and read off the answer !

Example: What is 5 /8 as a decimal ... ?

... get your calculator and type in "5 / 8 ="

http://www.mathsisfun.com/algebra/proportions.html

http://www.mathsisfun.com/scientific-calculator.html

http://www.mathsisfun.com/algebra/proportions.html



Fraction to Decimal

The answer should be 0.625

To convert a Fraction to a Decimal manually, follow these steps:

Step 1: Find a number you can multiply by the bottom of the fraction to make

it 10, or 100, or 1000, or any 1 followed by 0s.

Step 2: Multiply both top and bottom by that number.

Step 3. Then write down just the top number, putting the decimal point in the

correct spot (one space from the right hand side for every zero in the bottom

number)

Example 1: Express 3/4 as a Decimal

Step 1: We can multiply 4 by 25 to become 100


×25

3

=

75

4 100

×25

Step 3: Write down 75 with the decimal point 2 spaces from the right (because 100

has 2 zeros);

Answer = 0.75


Step 1: We have to multiply 16 by 625 to become 10,000


×625

3

=

1,875

16 10,000

×625



Fraction to Decimal

Step 3: Write down 1875 with the decimal point 4 spaces from the right (because

10,000 has 4 zeros);

Answer = 0.1875


Step 1: There is no way to multiply 3 to become 10 or 100 or any "1 followed by 0s",but we can calculate an approximate decimal by choosing to multiply by, say, 333


×333

1

=

333

3 999

×333

Step 3: Now, 999 is nearly 1,000, so let us write down 333 with the decimal point 3

spaces from the right (because 1,000 has 3 zeros):

Answer = 0.333 (accurate to only 3 decimal places !!)

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Fraction to Decimal.doc