Question

the decimal expansion of irrational numbers is

Answer 1

Answer:

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Step-by-step explanation:

A number which is not rational is called an irrational number.

We know that any rational number will have either terminating decimal expansion or a non teminating recurring decimal expansion.

Hence, an irrational number is a number which contains non-terminating and non-recurring decimal expansion.

Example:

0.1001100011100001111.........

Also,

√2 and √3 have non terminating non recurring decimal expansion

Hence, they are irrational numbers.

In the case of irrational numbers, the decimal expansion does not terminate, nor end with a repeating sequence. For example, the decimal representation of π starts with 3.14159, but no finite number of digits can represent π exactly, nor does it repeat.

Answer 2

Step-by-step explanation:

The decimal expansion of a number may terminate (in which case the number is called a regular number or finite decimal, e.g., ), eventually become periodic (in which case the number is called a repeating decimal, e.g., ), or continue infinitely without repeating (in which case the number is called irrational).