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Math 463

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Convert Decimals to Fractions
(Multiply top and bottom by 10 until you get a whole number, then simplify)
To convert a Decimal to a Fraction follow these steps:
Step 1: Write down the decimal divided by 1, like this: decimal/1
Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
Step 3: Simplify (or reduce) the fraction

Example: Express 0.75 as a fraction
Step 1: Write down 0.75 divided by 1:
0.75

1
Step 2: Multiply both top and bottom by 100 (there were 2 digits after the decimal point so that is 10×10=100):
× 100 0.75 = 75 1 100 × 100
(Do you see how it turns the top number into a whole number?)
Step 3: Simplify the fraction (this took me two steps): ÷5 ÷ 5 75 = 15 = 3 100 20 4 ÷5 ÷ 5 Answer = 3/4 Note: 75/100 is called a decimal fraction and 3/4 is called a common fraction !

Example: Express 0.625 as a fraction
Step 1: write down:
0.625

1
Step 2: multiply both top and bottom by 1,000 (there were 3 digits after the decimal point so that is 10×10×10=1,000)
625

1,000
Step 3: Simplify the fraction (it took me two steps here): ÷ 25 ÷ 5 625 = 25 = 5 1,000 40 8 ÷ 25 ÷ 5 Answer = 5/8 Example: Express 0.333 as a fraction
Step 1: Write down:
0.333

1
Step 2: Multiply both top and bottom by 1,000 (there were 3 digits after the decimal point so that is 10×10×10=1,000)
333

1,000
Step 3: Simplify Fraction:
Can't get any simpler! Answer = 333/1,000

But a Special Note:
If you really meant 0.333... (in other words 3s repeating forever which is called 3 recurring) then we need to follow a special argument. In this case we would write down:
0.333...

1
Then MULTIPLY both top and bottom by 3:
× 3 0.333... = 0.999... 1 3 × 3

And 0.999... = 1 (Does it? - see the 9 Recurring discussion for more if you are interested), so:
Answer = 1/3

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 ="
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
Step 2: Multiply top and bottom by 25:
×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
Example 2: Express 3/16 as a Decimal
Step 1: We have to multiply 16 by 625 to become 10,000
Step 2: Multiply top and bottom by 625:
×625

3 = 1,875 16 10,000 ×625
Step 3: Write down 1875 with the decimal point 4 spaces from the right (because 10,000 has 4 zeros);
Answer = 0.1875
Example 3: Express 1/3 as a Decimal
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
Step 2: Multiply top and bottom by 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 !!)

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
Because percent means "per 100", you can try to convert the fraction to ?/100 form.
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. Example 1: Express 3/4 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: Express 3/16 as a Percent
Step 1: We have to multiply 16 by 6.25 to become 100
Step 2: Multiply top and bottom by 6.25:
×6.25

3 = 18.75 16 100 ×6.25 Step 3: Write down 18.75 with the percentage sign:
Answer = 18.75%

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