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If x is a rational number whose decimal expension terminates then x can be expressed in the form p/q where p and q are co primes and the factorization of q is of the form 2^m5^n and where m and n are non negative integers. what is the meaning of 2^m5^n in this theorem?
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If x is a rational number whose decimal expension terminates then x ca...
Meaning of 2^m5^n in the Theorem
1. Factorization of q
In the context of the theorem, the expression 2^m5^n represents the factorization of q, the denominator in the rational number x = p/q. Here, q is a multiple of powers of 2 and 5, denoted by m and n respectively.
2. 2^m and 5^n
The terms 2^m and 5^n indicate that q can be expressed as a product of powers of 2 and 5. For example, if m = 2 and n = 3, then q = 2^2 * 5^3 = 1000.
3. Non-negative integers
The exponents m and n are non-negative integers, meaning they can take values of 0, 1, 2, 3, and so on. This ensures that the factorization of q consists only of powers of 2 and 5 without any negative exponents.
4. Co-primes
In addition to the factorization of q, the theorem states that p and q are co-primes, which means they have no common factors other than 1. This condition ensures that the rational number x is in its simplest form.
5. Decimal expansion terminates
The theorem specifically applies to rational numbers whose decimal expansion terminates, meaning the digits after the decimal point are finite. This restriction helps in identifying a specific form for rational numbers that can be expressed as p/q with co-primes p and q.
In conclusion, the expression 2^m5^n in the theorem signifies the factorization of the denominator q as a product of powers of 2 and 5, where m and n are non-negative integers. This factorization, along with the condition of co-primes p and q, characterizes rational numbers with terminating decimal expansions in a simplified form.
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If x is a rational number whose decimal expension terminates then x can be expressed in the form p/q where p and q are co primes and the factorization of q is of the form 2^m5^n and where m and n are non negative integers. what is the meaning of 2^m5^n in this theorem?
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If x is a rational number whose decimal expension terminates then x can be expressed in the form p/q where p and q are co primes and the factorization of q is of the form 2^m5^n and where m and n are non negative integers. what is the meaning of 2^m5^n in this theorem? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If x is a rational number whose decimal expension terminates then x can be expressed in the form p/q where p and q are co primes and the factorization of q is of the form 2^m5^n and where m and n are non negative integers. what is the meaning of 2^m5^n in this theorem? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x is a rational number whose decimal expension terminates then x can be expressed in the form p/q where p and q are co primes and the factorization of q is of the form 2^m5^n and where m and n are non negative integers. what is the meaning of 2^m5^n in this theorem?.
If x is a rational number whose decimal expension terminates then x can be expressed in the form p/q where p and q are co primes and the factorization of q is of the form 2^m5^n and where m and n are non negative integers. what is the meaning of 2^m5^n in this theorem? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If x is a rational number whose decimal expension terminates then x can be expressed in the form p/q where p and q are co primes and the factorization of q is of the form 2^m5^n and where m and n are non negative integers. what is the meaning of 2^m5^n in this theorem? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x is a rational number whose decimal expension terminates then x can be expressed in the form p/q where p and q are co primes and the factorization of q is of the form 2^m5^n and where m and n are non negative integers. what is the meaning of 2^m5^n in this theorem?.
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