Question

State true or false: The decimal form of an irrational number is non-terminating and

non-recurring.​

Answer 1

Answer:

A non-terminating, non-repeating decimal is a decimal number that continues endlessly, with no group of digits repeating endlessly. Decimals of this type cannot be represented as fractions, and as a result are irrational numbers. Pi is a non-terminating, non-repeating decimal.

Answer 2

TRUE, the decimal form of an irrational number is non-terminating and non-recurring.

This is because irrational numbers can't be expressed in the form of p/q where p and q are integers and q ≠ 0. If a number has finite decimal digits, it's possible to write such number in the form of p/q. Thus, when irrational numbers can't be written in this form, they can't have finite decimal digits. Similarly, if the digits in a decimal repeat, it's possible to write such number in p/q form.

Hence, decimal form of irrational numbers is always non-terminating and non-repeating.