SOLUTION: I have instructions on how to change fractions to decimals and do not understand the phrase in the instructions about power of ten. Here are the instuctions: Change the following

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Question 217635: I have instructions on how to change fractions to decimals and do not understand the phrase in the instructions about power of ten. Here are the instuctions:
Change the following fractions to decimals. Find Prime factors of denominator first. If the Fraction is repeating, use long division. If the fraction terminates make the denominator a POWER OF TEN by multiplying by the APPROPRIATE FACTORS.
Next question would be what does the phrase "appropriate factors" mean? Is the teacher talking about the prime factors? or some other factor to make the denominator a "power of ten"?
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
The directions you describe are a little confusing to me, too. Let me explain what I think they may be:
  • Every fraction can be converted to decimal form by long division.
  • Some fractions can be converted in a different way which may often be easier than long division. These fractions have denominators which can be changed to powers of ten. And once the denominator is a power of ten, the decimal form can be found by inspection.

From the directions you describe it sounds like your teacher prefers that you use the second procedure when possible.

Here's a procedure to use:
  1. Reduce the fraction, if possible.
  2. If the denominator is already a power of ten (10, 100, 1000, etc.), skip to step #7
  3. Factor the denominator into prime numbers. (Do not include 1.)
  4. If the prime factors include any numbers other than 2 or 5, then use long division.
  5. If the prime factors are just 2's and/or 5's, then figure out the "appropriate factors". The "appropriate factors" are the factors we need so that every factor of 2 can be paired with a factor of 5 and vice versa. Here are some examples:
    • Denominator: 2 "Appropriate factors": 5
    • Denominator: 5 "Appropriate factors": 2
    • Denominator: 2*2 "Appropriate factors": 5*5
    • Denominator: 2*2*2*5 "Appropriate factors": 5*5
    • Denominator: 5*5*5 "Appropriate factors": 2*2*2
    • Denominator: 2*2*2*5*5*5*5 "Appropriate factors": 2
  6. Multiply the numerator and denominator by the "appropriate factors". (Your denominator will be a 1 followed by as many zeros as you have pairs of 2*5 in the factored denominator.)
  7. To convert the "power-of-ten" denominator fraction into decimal:
    1. The number of zeros in the denominator is the number of decimal places.
    2. Write the numerator
    3. Position the decimal point so that you have the correct number of decimal places. This may require placing one or more zeros in front of the numerator

Here are some examples which I hope will make this clear:
1%2F20+=+1%2F%282%2A2%2A5%29+=+%285%2F5%29%281%2F%282%2A2%2A5%29%29+=+5%2F100+=+0.05

7%2F50+=+7%2F%282%2A5%2A5%29+=+%282%2F2%29%287%2F%282%2A5%2A5%29%29+=+14%2F100+=+0.14
5%2F6+=+5%2F%282%2A3%29 Use long division (because of the 3).