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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 is the definition for receding decimal?
If you mean a recurring or repeating decimal it's for example 2/3 = 0.666666 .... recuring 6
Is a decimal form of an irrational number a repeating decimal?
Not necessarily. Remember that the definition of an irrational number is a number that can't be expressed as a simple fraction. 2/3, for example, is rational by that definition even though its decimal form is a repeating decimal. Since irrational numbers cannot be written as fractions, they don't have fraction forms. So basically, numbers with repeating decimals are considered rational. Irrational numbers don't have repeating decimals.
Is 125 a repeating decimal?
No, 125 is not a repeating decimal. A repeating decimal is a decimal number that has a repeating pattern of digits after the decimal point. In the case of 125, it is a whole number and does not have any decimal places or repeating patterns. It can be written as 125.0000, but it is still a non-repeating decimal.
Why o10110111011110..this irrational?
It is a non-terminating, non-repeating decimal representation. That is a definition of irrational numbers.
