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Answer 1

Answer: (1) d, f     (2) c, d, f     (3) e, f      (4) a, b, c, d, f     (5) e, f

Step-by-step explanation:

a) Natural Numbers:            1, 2, 3, ...

b) Whole Numbers:          0, 1, 2, 3, ...     (add zero to the Natural numbers)

c) Integers:   ..., -3, -2, -1, 0, 1, 2, 3, ...   (add negatives to the Whole numbers)

d) Rationals: Add terminating and repeating decimals to Integers.

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e) Irrationals: Non-repeating decimals that are non-terminating.  This is its own category so cannot be a Rational number or above.

f) Real Numbers: ALL of the above (a - e) are Real numbers.

1) -5.2  has a terminating decimal so it is a RATIONAL number.

2) -4  is below zero so is an INTEGER which means it is also a RATIONAL #

3) -4.3212... is a non-terminating decimal so it is an IRRATIONAL number

4) $\sqrt4$ = 2 is a NATURAL number which means it is also a WHOLE number, INTEGER, and RATIONAL number.

5) $\sqrt7$  is a non-terminating decimal so it is an IRRATIONAL number