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Decide whether 52.123456789 is a rational number or not. If rational (in the form p/q), what can you say about the prime factors of q?
- a)Rational Number, Prime factor of q will be only 2.
- b)Rational Number, Prime factor of q will have a factor other than 2 or 5.
- c)Not rational number.
- d)Rational Number, Prime factors of q will have either 2 or 5 or both.
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Decide whether 52.123456789 is a rational number or not. If rational (...
It is rational because decimal expansion is terminating. Therefore, it can be expressed in p/q form where factors of q are of the form. and n and m are non-negative integers.
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Decide whether 52.123456789 is a rational number or not. If rational (...
Is 52.123456789 a rational number?
To determine if 52.123456789 is a rational number, we need to understand the characteristics of rational numbers.
Characteristics of Rational Numbers:
1. Rational numbers can be expressed as a fraction in the form of p/q, where p and q are integers and q is not equal to zero.
2. The decimal representation of a rational number is either terminating (ends) or repeating (has a repeating pattern).
Checking if 52.123456789 is a Rational Number:
In this case, 52.123456789 is a decimal number that does not terminate or repeat. However, we can convert it into a fraction to determine if it is a rational number.
Converting 52.123456789 into a Fraction:
To convert the decimal number 52.123456789 into a fraction, we can let x = 52.123456789 and multiply both sides by 10 to remove the decimal:
10x = 521.23456789
Now, subtract x from both sides:
10x - x = 521.23456789 - 52.123456789
Simplifying the equation:
9x = 469.111111101
To eliminate the repeating decimal, multiply both sides by 9:
81x = 4211
Divide both sides by 81:
x = 4211/81
Therefore, 52.123456789 can be expressed as the fraction 4211/81.
Prime Factors of the Denominator (q):
From the fraction 4211/81, we can see that the denominator (q) is 81. To find the prime factors of 81, we can use prime factorization.
Prime factorization of 81:
81 = 3^4
The prime factors of 81 are only 3. Therefore, the correct answer is:
d) Rational Number, Prime factors of q will have either 2 or 5 or both.
This means that the prime factors of the denominator (q) of the fraction 4211/81 can be either 2 or 5 or both.
To determine if 52.123456789 is a rational number, we need to understand the characteristics of rational numbers.
Characteristics of Rational Numbers:
1. Rational numbers can be expressed as a fraction in the form of p/q, where p and q are integers and q is not equal to zero.
2. The decimal representation of a rational number is either terminating (ends) or repeating (has a repeating pattern).
Checking if 52.123456789 is a Rational Number:
In this case, 52.123456789 is a decimal number that does not terminate or repeat. However, we can convert it into a fraction to determine if it is a rational number.
Converting 52.123456789 into a Fraction:
To convert the decimal number 52.123456789 into a fraction, we can let x = 52.123456789 and multiply both sides by 10 to remove the decimal:
10x = 521.23456789
Now, subtract x from both sides:
10x - x = 521.23456789 - 52.123456789
Simplifying the equation:
9x = 469.111111101
To eliminate the repeating decimal, multiply both sides by 9:
81x = 4211
Divide both sides by 81:
x = 4211/81
Therefore, 52.123456789 can be expressed as the fraction 4211/81.
Prime Factors of the Denominator (q):
From the fraction 4211/81, we can see that the denominator (q) is 81. To find the prime factors of 81, we can use prime factorization.
Prime factorization of 81:
81 = 3^4
The prime factors of 81 are only 3. Therefore, the correct answer is:
d) Rational Number, Prime factors of q will have either 2 or 5 or both.
This means that the prime factors of the denominator (q) of the fraction 4211/81 can be either 2 or 5 or both.
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Decide whether 52.123456789 is a rational number or not. If rational (in the form p/q), what can you say about the prime factors of q?a)Rational Number, Prime factor of q will be only 2.b)Rational Number, Prime factor of q will have a factor other than 2 or 5.c)Not rational number.d)Rational Number, Prime factors of q will have either 2 or 5 or both.Correct answer is option 'D'. Can you explain this answer?
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Decide whether 52.123456789 is a rational number or not. If rational (in the form p/q), what can you say about the prime factors of q?a)Rational Number, Prime factor of q will be only 2.b)Rational Number, Prime factor of q will have a factor other than 2 or 5.c)Not rational number.d)Rational Number, Prime factors of q will have either 2 or 5 or both.Correct answer is option 'D'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Decide whether 52.123456789 is a rational number or not. If rational (in the form p/q), what can you say about the prime factors of q?a)Rational Number, Prime factor of q will be only 2.b)Rational Number, Prime factor of q will have a factor other than 2 or 5.c)Not rational number.d)Rational Number, Prime factors of q will have either 2 or 5 or both.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Decide whether 52.123456789 is a rational number or not. If rational (in the form p/q), what can you say about the prime factors of q?a)Rational Number, Prime factor of q will be only 2.b)Rational Number, Prime factor of q will have a factor other than 2 or 5.c)Not rational number.d)Rational Number, Prime factors of q will have either 2 or 5 or both.Correct answer is option 'D'. Can you explain this answer?.
Decide whether 52.123456789 is a rational number or not. If rational (in the form p/q), what can you say about the prime factors of q?a)Rational Number, Prime factor of q will be only 2.b)Rational Number, Prime factor of q will have a factor other than 2 or 5.c)Not rational number.d)Rational Number, Prime factors of q will have either 2 or 5 or both.Correct answer is option 'D'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Decide whether 52.123456789 is a rational number or not. If rational (in the form p/q), what can you say about the prime factors of q?a)Rational Number, Prime factor of q will be only 2.b)Rational Number, Prime factor of q will have a factor other than 2 or 5.c)Not rational number.d)Rational Number, Prime factors of q will have either 2 or 5 or both.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Decide whether 52.123456789 is a rational number or not. If rational (in the form p/q), what can you say about the prime factors of q?a)Rational Number, Prime factor of q will be only 2.b)Rational Number, Prime factor of q will have a factor other than 2 or 5.c)Not rational number.d)Rational Number, Prime factors of q will have either 2 or 5 or both.Correct answer is option 'D'. Can you explain this answer?.
Solutions for Decide whether 52.123456789 is a rational number or not. If rational (in the form p/q), what can you say about the prime factors of q?a)Rational Number, Prime factor of q will be only 2.b)Rational Number, Prime factor of q will have a factor other than 2 or 5.c)Not rational number.d)Rational Number, Prime factors of q will have either 2 or 5 or both.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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ample number of questions to practice Decide whether 52.123456789 is a rational number or not. If rational (in the form p/q), what can you say about the prime factors of q?a)Rational Number, Prime factor of q will be only 2.b)Rational Number, Prime factor of q will have a factor other than 2 or 5.c)Not rational number.d)Rational Number, Prime factors of q will have either 2 or 5 or both.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Class 10 tests.
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