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The fraction is rational, the repeating decimal is not. A fraction is a fraction and a repeating decimal is a repeating decimal. They are different representaions of a quantity. One is finite the other is not. It is unreasonable to say a repeating decimal is a fraction and therefore the repeating decimal is rational. The repeating decimal is what it is, albeit derived from a fration, it is not a fration. You can hold 1/3 of a Pizza in your hands but you cannot hold .333333... of a pizza in your hands. It is literally irrational for you to say that you can. Theoretically, if you accept that you can always add another decimal place to any decimal number, and that inner space is infinite, without limits, then my point is valid. .333333... is moving infinitly closer to 1/3 without ever getting there, and the more 3's are piled on, the closer it gets, but is forever approaching 1/3, the same as the universe of decimals never arrives at zero. A pizza the size of .333333... is a work in progress, never terminating at any size at all, but continually sizing itself towards 1/3 forever - quite irrational, possessing a character equal to the famously irrational pi. 1/3 of a pizza is precise, easily sliced, finite, rational, and I'll have mine with sliced tomatoes and a caffeine-free, diet root beer.
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A repeating decimal is an irrational number?
Actually, a repeating decimal is not necessarily an irrational number. A repeating decimal is a decimal number that has a repeating pattern of digits after the decimal point. While some repeating decimals can be irrational, such as 0.1010010001..., others can be rational, like 0.3333... which is equal to 1/3. Irrational numbers are numbers that cannot be expressed as a simple fraction, and they have non-repeating, non-terminating decimal representations.
Is .3333 repeating a rational or irrational number?
Rational
Is 0.23 repeating a rational irrational or a whole number or an integer?
Rational number
Is 75.082106 repeating rational or irrational?
The number 75.082106 with a repeating decimal is rational. A rational number can be expressed as a fraction of two integers, where the denominator is not zero. In this case, the repeating decimal can be written as a fraction, making it a rational number. Irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal expansions.
Is 4.13 repeating rational number or irrational number?
It is a rational number because it can be expressed as a fraction.
Is -3 an irrational or rational number?
If a number can be expressed as a terminating or repeating decimal then it is rational (and conversely). So -3 is rational.
Can a rational number be repeating decimal?
Yes, a rational number can be a repeating decimal. A repeating decimal is a decimal in which one or more digits repeat infinitely. For example, 1/3 is a rational number that can be written as the repeating decimal 0.333...
Is negative 4 over 3 rational or irrational?
Rational -1.(3 repeating) Any repeating decimals are rational. However, a number such as pi (3.141592654...) does not repeat or end.
What is the Rational number between -3 and -2 with a digit repeating?
-1
Is 0.88 repeating a rational number?
Is 0.88 repeating a rational number
Is 0.666666666 rational or rational?
If that is repeating 6 then it is a rational number because it can be expressed as a fraction in the form of 2/3
Is 5.75 repeating a rational number or irrational?
It is a rational number.
Is a rational number a repeating decimal?
All repeating decimals are rational numbers. Not all rational numbers are repeating decimals.
Is 2.6 repeating a rarional number?
2.6666...repeating is a rational number because it can be expressed as a fraction in the form of 8/3
Why is a repeating decimal a rational number?
A rational number is a number that can eb expressed as a ratio of two numbers. 1/3 is a rational number, with a decimal representation of 0.333333 ... .
A repeating decimal is an irrational number?
Actually, a repeating decimal is not necessarily an irrational number. A repeating decimal is a decimal number that has a repeating pattern of digits after the decimal point. While some repeating decimals can be irrational, such as 0.1010010001..., others can be rational, like 0.3333... which is equal to 1/3. Irrational numbers are numbers that cannot be expressed as a simple fraction, and they have non-repeating, non-terminating decimal representations.
Is a repeating decimal sometimes a rational number?
Repeating decimals are always rational.
