Subject: Occuring pattern in repeating decimals
Who is asking: Student
Hi, I'm working on a project for school. The theory I choose was "When turned into a fraction, a repeating decimal has a denometor that is a multiple of three." I have a couple of questions about this topic. My first question is, have you ever heard of this, and what can you tell me about it? My second question is, when I was testing this theory I came across .999... now, when this is a fraction it is 9/9 which is equal to one. The denometor is a multiple of 3, but it's a whole number. I don't understand how a decimal can be equal to a whole number since a decimal is a piece of a whole number. Please don't just show me a math problem, I don't want to see a math problem. I want to see an explanation of this theory and the decimal .999...
I have never heard this theory before. My first reaction is that I don't beleive that it is true. I would first look for a counterexample. Try some fractions 1/d where d is not a multiple of 3, write them in decimal form and see if you can find one which is repeating. I suppose that you might say that
1/2 = 0.5000000...
is repeating, but I expect you want the repeating part to be something other than zero.
I think that you have answered the second question yourself. You say that "I don't understand how a decimal can be equal to a whole number since a decimal is a piece of a whole number." A "decimal" is one way to express a fractional part of something, another way is to use a common fraction.
1/2 is one half of 1
2/3 is two thirds of 1
3/4 is three quarters of 1
4/5 is four fifths of 1
9/9 is nine ninths of 1
9/9 is one of the many ways we can express the number 1.
0.999... is another.
I know you don't want to see a "math problem" but I encourage you to look at the answers we gave to similar questions by Andrew and Joan.