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Fraction to Decimal to Percent Conversions

Date: 10/29/2001 at 17:57:48
From: Jacob G
Subject: Decimal TO fraction TO percent


I am in 7th grade and my teacher requires us to be able to convert 
fractions, percents, and decimals all together rather than converting 
a percent to a fraction OR a decimal as you have shown in your 
examples. I already understand that. What I am confused about is 

           a decimal TO a fraction TO a Percent

  "OR"     a percent TO a decimal  TO a fraction

           a decimal TO a percent TO  a fraction

My teacher expects us to covert all three in any order and I cannot 
find how to do that ANYWHERE. Can you show some step-by-step examples?  

Thank you, 

Date: 10/29/2001 at 22:51:54
From: Doctor Peterson
Subject: Re: Decimal TO fraction TO percent

Hi, Jacob.

I'm a little confused. Are you saying you don't know how to do ANY of 
these six conversions, or just that you can't do them one after 
another? Surely we've shown you at least half of them in our FAQ:

   Fractions, Decimals, Percentages   

But let's do them all:

Decimal to percent:

    Multiply by 100%, by moving the decimal point two places to the
    right and following it with "%":

    0.75 -> 0.75 * 100% = 75%

Percent to fraction:

    Replace "%" with "/100", and simplify if required:

    75% -> 75/100 = 3/4

Fraction to decimal:

    Divide numerator by denominator, using as many decimal places as 

    3/4 -> 3.00 divided by 4 = 0.75

Decimal to fraction:

    Remove the decimal point to form the numerator, and for the
    denominator use 1 with as many zeros as the decimal places you

            0.75    75    3
    0.75 -> ---- = --- = ---
            1.00   100    4

Fraction to percent:

    Multiply numerator by 100% and divide by denominator:

    3/4 -> 300% divided by 4 = 75%

Percent to decimal:

    Divide by 100% by taking off the "%" and moving the decimal point 
    two places to the left:

    75% -> 75% / 100% = 0.75

Does that cover everything? For harder cases of converting decimal to 
fraction, see the FAQ.

- Doctor Peterson, The Math Forum   
Associated Topics:
Middle School Fractions

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