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The decimal representation of an irrational number is
- a)neither terminating nor repeating
- b)either terminating or non-repeating
- c)always terminating
- d)always non-terminating
Correct answer is option 'A'. Can you explain this answer?
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The decimal representation of an irrational number isa)neither termina...
It means that a irrational number should be non repeating and non terminating, if it is non terminating recurring ( repeating) or it's terminating then it is not a irrational number.
example of irrational number: √2, √3 ,π etc.
example of irrational number: √2, √3 ,π etc.
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The decimal representation of an irrational number isa)neither termina...
Decimal Representation of Irrational Numbers
Irrational numbers are numbers that cannot be expressed as a ratio of two integers. Examples include √2, π, and e.
Decimal representation of a number is a way of expressing the number using the base-10 number system. It is usually represented as a sequence of digits, with a decimal point separating the integer part from the fractional part.
Now, coming to the question, the statement "the decimal representation of an irrational number is neither terminating nor repeating" is true. This is because:
Non-terminating decimal representation
An irrational number, by definition, cannot be expressed as a ratio of two integers. Therefore, its decimal representation cannot be expressed as a finite or terminating decimal. For example:
- √2 = 1.41421356...
- π = 3.14159265...
- e = 2.71828182...
As you can see, the decimal representation of these irrational numbers goes on indefinitely without repeating or terminating.
Non-repeating decimal representation
In addition, the decimal representation of an irrational number cannot be expressed as a repeating decimal. A repeating decimal is a decimal in which a sequence of digits repeats indefinitely. For example:
- 1/3 = 0.33333333...
- 2/7 = 0.285714285714285714...
Again, you can see that the decimal representation of these rational numbers repeats indefinitely.
Conclusion
In conclusion, the decimal representation of an irrational number is neither terminating nor repeating. It goes on indefinitely without any pattern or repetition. This is what makes irrational numbers unique and interesting.
Irrational numbers are numbers that cannot be expressed as a ratio of two integers. Examples include √2, π, and e.
Decimal representation of a number is a way of expressing the number using the base-10 number system. It is usually represented as a sequence of digits, with a decimal point separating the integer part from the fractional part.
Now, coming to the question, the statement "the decimal representation of an irrational number is neither terminating nor repeating" is true. This is because:
Non-terminating decimal representation
An irrational number, by definition, cannot be expressed as a ratio of two integers. Therefore, its decimal representation cannot be expressed as a finite or terminating decimal. For example:
- √2 = 1.41421356...
- π = 3.14159265...
- e = 2.71828182...
As you can see, the decimal representation of these irrational numbers goes on indefinitely without repeating or terminating.
Non-repeating decimal representation
In addition, the decimal representation of an irrational number cannot be expressed as a repeating decimal. A repeating decimal is a decimal in which a sequence of digits repeats indefinitely. For example:
- 1/3 = 0.33333333...
- 2/7 = 0.285714285714285714...
Again, you can see that the decimal representation of these rational numbers repeats indefinitely.
Conclusion
In conclusion, the decimal representation of an irrational number is neither terminating nor repeating. It goes on indefinitely without any pattern or repetition. This is what makes irrational numbers unique and interesting.
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The decimal representation of an irrational number isa)neither terminating nor repeatingb)either terminating or non-repeatingc)always terminatingd)always non-terminatingCorrect answer is option 'A'. Can you explain this answer?
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