The decimal expansion of the number 2 is(A) a finite decimal(B) 1.41421(C) non-terminating recurring(D) non-terminating non-recurring

To determine the appropriate classification of the decimal expansion of the number 2, we can analyze its properties in relation to finite and infinite decimal expansions.

1. Understanding Decimal Expansions:

   • A finite decimal is a number that has a fixed number of digits after the decimal point, like 0.75 or 1.5.
   • A non-terminating recurring decimal repeats a sequence of digits indefinitely, such as 0.333... or 1.666...
   • A non-terminating non-recurring decimal does not have a repeating sequence and goes on indefinitely, like the decimal expansion of π (3.14159...).

2. Analyzing the Number 2:

   • The number 2 can be expressed as a decimal: 2.0. This shows it has a finite representation with one digit following the decimal point.
   • Since it terminates after one decimal place, it does not have a recurring or non-recurring aspect.

3. Definitions of Options:

   • (A) A finite decimal: This correctly describes the number 2, as its decimal representation ends.
   • (B) 1.41421: This is the decimal representation of √2, not relevant to the discussion of 2.
   • (C) Non-terminating recurring: This implies a decimal that repeats indefinitely, which does not apply to 2.
   • (D) Non-terminating non-recurring: Like π, this does not apply to the number 2.

Based on the analysis:

Final Answer

The decimal expansion of the number 2 is (A) a finite decimal.