The decimal 5.123123312333... shows no fixed repeating pattern. What type of number is it?
Answer and explanation
Correct answer: Irrational number
A decimal expansion that is non-terminating and non-repeating represents an irrational number. Rational numbers always have decimal expansions that either terminate or eventually repeat a fixed block. The given expansion 5.123123312333... shows no fixed repeating block, so it is irrational. The closest distractor, 'rational number', is incorrect because a rational decimal must exhibit a repeating pattern if it does not terminate. Exam tip: to test quickly, look for a consistent repeating block—if none exists, the number is irrational.
Frequently asked questions
What is the correct answer to this question?
Irrational number
Why is this the correct answer?
A decimal expansion that is non-terminating and non-repeating represents an irrational number. Rational numbers always have decimal expansions that either terminate or eventually repeat a fixed block. The given expansion 5.123123312333... shows no fixed repeating block, so it is irrational. The closest distractor, 'rational number', is incorrect because a rational decimal must exhibit a repeating pattern if it does not terminate. Exam tip: to test quickly, look for a consistent repeating block—if none exists, the number is irrational.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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