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Write the condition to be satisfied by q so that a rational number p/q has a terminating decimal expansion. guzz ans fast.
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Write the condition to be satisfied by q so that a rational number p/q...
q must be in the form of 2 power m * 5 power n. where m and n must be real numbers and p/q must be in simple form
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Write the condition to be satisfied by q so that a rational number p/q...
Condition for Terminating Decimal Expansion of Rational Number
To determine whether a rational number p/q will have a terminating decimal expansion, we need to consider the denominator q. The condition for q to satisfy for the decimal expansion of p/q to be terminating is:
1. Prime Factorization of Denominator
- The denominator q should have a prime factorization of the form 2^n * 5^m, where n and m are non-negative integers. This means that q should only have 2s and/or 5s in its prime factorization.
2. Absence of Other Prime Factors
- The denominator q should not have any other prime factors apart from 2 and 5. If q has a prime factor other than 2 or 5, the decimal expansion of p/q will be repeating.
3. Examples
- For example, the rational number 3/8 does not have a terminating decimal expansion because the denominator 8 has a prime factorization of 2^3. On the other hand, the rational number 15/40 has a terminating decimal expansion because the denominator 40 can be expressed as 2^3 * 5^1.
By ensuring that the denominator q satisfies the above conditions, we can determine whether a rational number p/q will have a terminating decimal expansion.
To determine whether a rational number p/q will have a terminating decimal expansion, we need to consider the denominator q. The condition for q to satisfy for the decimal expansion of p/q to be terminating is:
1. Prime Factorization of Denominator
- The denominator q should have a prime factorization of the form 2^n * 5^m, where n and m are non-negative integers. This means that q should only have 2s and/or 5s in its prime factorization.
2. Absence of Other Prime Factors
- The denominator q should not have any other prime factors apart from 2 and 5. If q has a prime factor other than 2 or 5, the decimal expansion of p/q will be repeating.
3. Examples
- For example, the rational number 3/8 does not have a terminating decimal expansion because the denominator 8 has a prime factorization of 2^3. On the other hand, the rational number 15/40 has a terminating decimal expansion because the denominator 40 can be expressed as 2^3 * 5^1.
By ensuring that the denominator q satisfies the above conditions, we can determine whether a rational number p/q will have a terminating decimal expansion.
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Write the condition to be satisfied by q so that a rational number p/q has a terminating decimal expansion. guzz ans fast. 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 Write the condition to be satisfied by q so that a rational number p/q has a terminating decimal expansion. guzz ans fast. covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Write the condition to be satisfied by q so that a rational number p/q has a terminating decimal expansion. guzz ans fast..
Write the condition to be satisfied by q so that a rational number p/q has a terminating decimal expansion. guzz ans fast. 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 Write the condition to be satisfied by q so that a rational number p/q has a terminating decimal expansion. guzz ans fast. covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Write the condition to be satisfied by q so that a rational number p/q has a terminating decimal expansion. guzz ans fast..
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