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The decimal expansion of a rational number is always:
- a)Non-terminating
- b)Non-terminating and non-repeating
- c)Terminating or non-terminating repeated
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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The decimal expansion of a rational number is always:a)Non-terminatin...
The decimal expansion of a rational number always either terminates after finitely many digits or begins to repeat the same sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number.
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The decimal expansion of a rational number is always:a)Non-terminatin...
Decimal expansion of an irrational number is non-terminating NON-REPEATING
decimal expansion of a rational number is terminating or non-terminating REPEATING
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The decimal expansion of a rational number is always:a)Non-terminatin...
Decimal Expansion of a Rational Number
Rational numbers are numbers that can be expressed as a fraction where the numerator and denominator are integers. When we try to represent a rational number in decimal form, the decimal expansion can either terminate or be non-terminating repeating.
Terminating Decimal
- A rational number has a terminating decimal expansion if when divided, the remainder becomes zero at some point.
- For example, 1/4 = 0.25, where the decimal expansion terminates after 2 decimal places.
Non-Terminating Repeating Decimal
- A rational number has a non-terminating repeating decimal expansion if the division does not end with a remainder of zero and a pattern of digits repeats indefinitely.
- For example, 1/3 = 0.333..., where the digit 3 repeats infinitely.
Conclusion
- Therefore, the decimal expansion of a rational number can be either terminating or non-terminating repeating.
- It is important to note that irrational numbers, such as the square root of 2, have non-terminating non-repeating decimal expansions.
- Understanding the decimal expansion of rational numbers is crucial in various mathematical calculations and applications.
Rational numbers are numbers that can be expressed as a fraction where the numerator and denominator are integers. When we try to represent a rational number in decimal form, the decimal expansion can either terminate or be non-terminating repeating.
Terminating Decimal
- A rational number has a terminating decimal expansion if when divided, the remainder becomes zero at some point.
- For example, 1/4 = 0.25, where the decimal expansion terminates after 2 decimal places.
Non-Terminating Repeating Decimal
- A rational number has a non-terminating repeating decimal expansion if the division does not end with a remainder of zero and a pattern of digits repeats indefinitely.
- For example, 1/3 = 0.333..., where the digit 3 repeats infinitely.
Conclusion
- Therefore, the decimal expansion of a rational number can be either terminating or non-terminating repeating.
- It is important to note that irrational numbers, such as the square root of 2, have non-terminating non-repeating decimal expansions.
- Understanding the decimal expansion of rational numbers is crucial in various mathematical calculations and applications.
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The decimal expansion of a rational number is always:a)Non-terminatingb)Non-terminating and non-repeatingc)Terminating or non-terminating repeatedd)None of theseCorrect answer is option 'C'. Can you explain this answer?
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