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The decimal representation of a rational number is
- a)either terminating or repeating
- b)always terminating
- c)always non-terminating
- d)either terminating or non-repeating
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The decimal representation of a rational number isa)either terminating...
Any rational number (that is, a fraction in lowest terms) can be written as either a terminating decimal or a repeating decimal . Just divide the numerator by the denominator . ... Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimal.
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Most Upvoted Answer
The decimal representation of a rational number isa)either terminating...
Explanation:
Rational Number: A number which can be represented in the form of p/q, where p and q are integers and q is not equal to zero is called a rational number.
Terminating Decimal: A decimal which terminates after a finite number of digits is called a terminating decimal. For example, 0.5, 0.25, 0.125, 0.0625, and so on.
Non-Terminating Decimal: A decimal which does not terminate after a finite number of digits is called a non-terminating decimal. For example, 0.3333..., 0.6666..., 0.142857142857..., and so on.
Non-Terminating Non-Repeating Decimal: A decimal which does not terminate and also does not repeat any pattern of digits after a certain point is called a non-terminating non-repeating decimal. For example, pi (π) = 3.14159265358979323846..., e = 2.71828182845904523536..., and so on.
Decimal Representation of Rational Number: When we divide a rational number by a non-zero integer, we get a decimal representation of that rational number.
Conclusions:
From the given options, we can conclude that:
Rational Number: A number which can be represented in the form of p/q, where p and q are integers and q is not equal to zero is called a rational number.
Terminating Decimal: A decimal which terminates after a finite number of digits is called a terminating decimal. For example, 0.5, 0.25, 0.125, 0.0625, and so on.
Non-Terminating Decimal: A decimal which does not terminate after a finite number of digits is called a non-terminating decimal. For example, 0.3333..., 0.6666..., 0.142857142857..., and so on.
Non-Terminating Non-Repeating Decimal: A decimal which does not terminate and also does not repeat any pattern of digits after a certain point is called a non-terminating non-repeating decimal. For example, pi (π) = 3.14159265358979323846..., e = 2.71828182845904523536..., and so on.
Decimal Representation of Rational Number: When we divide a rational number by a non-zero integer, we get a decimal representation of that rational number.
Conclusions:
From the given options, we can conclude that:
- Option A: Terminating decimals can be the decimal representation of a rational number. Hence, option A is incorrect.
- Option B: Sometimes rational numbers have terminating decimals, but not always. Hence, option B is incorrect.
- Option C: Rational numbers can have non-terminating decimals, but not always non-terminating. Hence, option C is incorrect.
- Option D: A rational number can have a non-terminating non-repeating decimal representation. Hence, option D is correct.
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Community Answer
The decimal representation of a rational number isa)either terminating...
Yes becoz as we know rational number is in the form of a/b where a and b r integers and b donot equal to 0....so a{b must be divided if they r dividing the they will give us terminating,repeating,non repeating,either they will be non terminating....
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