Question

The decimal expansion of a rational number can never be ________​

Answer 1

The decimal expansion of a rational number can never be ________

Answer:

non-terminated

Answer 2

Answer :- Non terminating non repeating .

Explanation :-

we know that,

• A number which can be written in the form of p/q where q ≠ 0 is called a rational numbers .

Terminating decimal numbers :- Number with finite decimal places .

→ (1/2) = 0.5

→ (33/40) = 0.825

Since , these numbers can be written in the form of p/q and q is also not equal to zero , therefore, they are rational numbers .

Non Terminating decimal numbers :- Numbers with no end term .

→ (1/9) = 0.11111____

→ (1/3) = 0.3333____

Since , these numbers can be written in the form of p/q and q is also not equal to zero , therefore, they are rational numbers .

Repeating decimal numbers :- Numbers in which a set of terms after decimal repeats uniformly .

→ (2/3) = 0.666______

→ (12/99) = 0.121212_____

→ (105/999) = 0.105105____

Since , these numbers can be written in the form of p/q and q is also not equal to zero , therefore, they are rational numbers . These numbers are also called as non terminating repeating decimal numbers .

Non Terminating non repeating decimal numbers :- Numbers in which terms after decimal repeats without any pattern of repetition of digits .

→ 0.12122122212222_____

→ √2 = 1.41421356______

since these numbers can not be written in the form of p/q , therefore, they are not rational numbers .

Hence, we can conclude that, The decimal expansion of a rational number can never be non terminating non repeating .

Learn more :-

prove that √2-√5 is an irrational number

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