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A rational number is one which can be expressed as one integer over another.
A decimal is a rational number if:
- It terminates; or
- it ends with a repeating (cycle of) digit(s)
eg 0.5, 0.333...., 0.181818..., 0.1666... are all rational numbers which can be expressed as one integer over another:
0.5 = 1/2
0.333... = 1/3
0.181818... = 2/11
0.1666... =1/6
Any number which is not rational is an irrational number; its decimal representation does not terminate nor does it end with a repeating (cycle of) digit(s).
eg 0.1234567891011121314... (the counting numbers strung together after a decimal point)
π = 3.1415926535897932... (the ratio of the circumference to the diameter of a circle)
e = 2.71828218284590452... (Euler's number, the base of natural logarithms)
√2 = 1.414213562373095...
are all Irrational Numbers
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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 are the difference between decimal in rational and decimal in irrational?
A decimal rational number can be expressed as a fraction A decimal irrational number can not be expressed as a fraction
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.
Why every rational number can be represented by either a terminating decimal or a repeating decimal?
That is the definition of a rational number.
What can you say about the decimal expansion of any rational number?
If its a rational number then its decimal equivalent can be expressed as a fraction
