Question

Write all the names that apply to each number .

Answer 1

Definitions:
1. A real number can be represented on a number line.
2. A rational number can be represented as a fraction, with both the numerator and denominator as integers. The denominator cannot be zero.
3. An irrational number has decimals that go on indefinitely.
4. An integer is a real number that is countable.
5. A repeating decimal has a group of numbers that repeat indefinitely as decimals. 
6. A complex number involves the use of the quantity i, defined as i² = -1.

Answers:
a. 7/8
   Real, Rational.

b. √36
    Real, Rational because its value is +6 or -6.

c. √24
   Real, Irrational.

d. 0.75
    Real, rational because 0.75 = 3/4.

e. 0
    Real, rational

f. √(-100)
   Complex, because √(-1) * √100 = +/- i√100

g. $5.\overline{45}$
   Irrational, Repeating decimal because
   $5.\overline{45} = 5.4545454545 ...$

h -18/6
   Real, Integer, Rational because -18/6 = -3.