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Why decimal is considered as rational number?
A decimal need not be a rational. A non-terminating, non recurring decimal is an irrational number. Only a terminating decimal or a recurring decimal is rational and that is because such a number can be expressed as a ratio of two integers.
Is decimal a rational number?
It depends. A terminating decimal is a rational number. A decimal which, after a finite number of places, becomes a repeating (or recurrent) decimal is also a rational number. A decimal that is not terminating, nor [eventually] settles into a recurring pattern is not a rational number. Note that the decimal need not become recurring immediately.
What number has one repeated prime factor?
It could be 1/3 when expressed as a decimal is 0.333333 ..... recurring
What does it mean for a number to be rational?
That it can be expressed as a ratio (hence rational) of two integers, the denominator being positive.In decimal representation, it is a necessary and sufficient condition that the number can be expressed as either a terminating decimal or one that becomes a recurring decimal after a finite number of digits.
Is 13.001001001 a rational or irrational number and why?
A rational number is a number that can be expressed as a fraction. This means it can either be a terminating decimal or a recurring decimal. A terminating decimal is a decimal that doesn't recur (repeat for ever). A recurring decimal is a decimal that repeats a pattern of numbers after the decimal point. A good example of this is 1/3. 1/3 = 0.333333.... it is a rational number 13.001001001 is a rational number. Either you meant it to recur or not it makes no difference. 13.001001001 = 13 + 1001001/1000000000 as a terminating decimal 13.001001001....... = 12988/999 as a recurring decimal ---- Examples of numbers that are not rational: sqrt(2), pi, exp they are irrational as they cannot be expressed as fractions.
