The decimal expansion of √2a. Finite decimal b. 1.4121c. non terminating recurring d. non-terminating non-recurring

It seems like you're asking for the nature of the decimal expansion of √2 and the classification of 1.4121. Here are the answers:

a. The decimal expansion of √2 is non-terminating and non-recurring. This is because √2 is an irrational number, and the decimal expansions of irrational numbers neither terminate nor recur.

b. 1.4121 is a finite decimal. This is because it has a definite number of digits after the decimal point and does not go on indefinitely.

c. A non-terminating recurring decimal is a decimal that does not end but has a pattern that repeats indefinitely. An example of this is 1/3 = 0.3333...

d. A non-terminating non-recurring decimal is a decimal that goes on indefinitely without any repeating pattern. An example of this is the number pi (π) = 3.141592653589793...