Fractions help!

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rymt15

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Hello everyone,
I'm studying the Mathematics O'Level on my own as I currently can't afford private lessons. I'm following next year's syllabus and so far I've been doing great.
However I'm in the last section of Fractions and the syllabus states the following:

''Understand that fractions which in their lowest termsare of the form m/(2p5q) are non-recurring (m, p, andq are non-negative integers or zero).''

I know it may sound stupid but I can't understand what I should be understanding... if that makes sense.
Thank you!:(:confused:
 
rymt15 said:
Hello everyone,
I'm studying the Mathematics O'Level on my own as I currently can't afford private lessons. I'm following next year's syllabus and so far I've been doing great.
However I'm in the last section of Fractions and the syllabus states the following:

''Understand that fractions which in their lowest termsare of the form m/(2p5q) are non-recurring (m, p, andq are non-negative integers or zero).''

I know it may sound stupid but I can't understand what I should be understanding... if that makes sense.
Thank you!:(:confused:
Click to expand...
You give no context, and I think what you mean is

\(\displaystyle \dfrac{m}{2^p5^q} \text {, where } m,\ p, \text { and } q \text { are non-negative integers.}\)

Is that correct? 2p5q is just an odd way to write 10pq.

Absent context, I think they are saying that those fractions ( and only those fractions) can be expressed EXACTLY in decimal form.

EDIT: I see that Dr. Peterson reads your question as I do. Nevertheless, I think the statement that you are asking about is crafted very poorly: if what was meant was "terminating" then "non-recurring" is confusing. Every real number can, in principle, be expressed exactly in an infinite number of decimals. For example, 1/2 can be expressed as 0.50000.... with zeroes going on forever. Similarly, 1/3 can be expressed as 0.3333333.... with threes going on forever. In practice, however, 1/2 can also be expressed in decimal form exactly in a finite number of digits as 0.5 whereas 1/3 can never be expressed exactly in decimal form in a finite number of digits.
 
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It is saying that fractions that can be represented as m/(2^p 5^q), that is, whose denominator's only prime factors are 2 and 5, are terminating decimals (that is, you can write them with only a finite number of decimal places).

Examples are 1/50 = 1/(2^1 * 5^2) and 1/20 = 1/(2^2 * 5^1); a fraction like 1/35 = 1/(5*7) has a prime factor other than 2 and 5, so it can't be written as a terminating decimal.

Here is an explanation.
 
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