Rational or Irrational? (***WITH EXPLANATIONS***)

Irrational. The number -0.123456789101112... is an irrational number, because it is a non-terminating, non-repeating decimal. In addition, it cannot be expressed as the ratio of two integers (as a simple fraction or ratio).

-0.123456789101112...

Rational. The number -1 is a rational number, because it is an integer. It can also be written as a quotient of two integers in the form a/b (b cannot be equal to 0). -1 can further be classified into the rational number subsets of integers and whole numbers.

-1

Rational. The number 1/8 is a rational number, because it is a quotient of two integers in the form a/b (b cannot be equal to 0) and is a terminating decimal. 1/8 = 0.125

1/8

Rational. The number 11/9 is a rational number, because it is a quotient of two integers in the form a/b (b cannot be equal to 0), and it is a repeating decimal. 11/9 = 1.222...

11/9

Rational. The number -1.09 is a rational number, because it is a terminating decimal and can be written as a quotient of two integers in the form a/b (b cannot be equal to 0). -1.09 = -1_9/100 = -109/100

-1.09

Rational. The number -27/9 is a rational number, because it is a quotient of two integers in the form a/b (b cannot be equal to 0), it is a terminating decimal, and it is an integer. -27/9 = -3.0 = -3

-27/9

Rational. The number -2u1/3 is a rational number, because it is a quotient of two integers in the form a/b (b cannot be equal to 0) and is a repeating decimal. -2_1/3 = -7/3 = -2.333...

-2u1/3

Rational. The number 0 is a rational number, because it is an integer and a whole number. It can also be written as a quotient of two integers in the form a/b (b cannot be equal to 0). 0 can further be classified into the rational number subsets of integers and whole numbers.

0

Irrational. The number 0.151151115... is an irrational number, because it is a non-terminating, non-repeating decimal. In addition, it cannot be expressed as the ratio of two integers (as a simple fraction or ratio).

0.151151115...

Rational. The number 0.333... is a rational number, because it is a repeating decimal and can be written as a quotient of two integers in the form a/b (b cannot be equal to 0). 0.333... = 1/3

0.333...

Rational. The number 0.5 is a rational number, because it is a terminating decimal and can be written as a quotient of two integers in the form a/b (b cannot be equal to 0). 0.5 = 1/2

0.5

Rational. The number 1u2/5 is a rational number, because it is a quotient of two integers in the form a/b (b cannot be equal to 0) and is a terminating decimal. 1u2/5 = 7/5 = 1.4

1u2/5

Rational. The number 2/3 is a rational number, because it is a quotient of two integers in the form a/b (b cannot be equal to 0) and is a repeating decimal. 2/3 = 0.666...

2/3

undefined (N/O.."NO")

3/0 or 3÷0

Rational. The number 5 is a rational number, because it is an integer, a whole number, and a natural number. It can also be written as a quotient of two integers in the form a/b (b cannot be equal to 0). 5 can further be classified into the rational number subsets of integers , whole numbers, and natural numbers.

5

Rational. The number 5 - √4 is a rational number, because it is an integer, a whole number, and a natural number. It can also be written as a quotient of two integers in the form a/b (b cannot be equal to 0). 5 - √4 = 5 - 2 = 3

The value represented by 5 - √4.

Irrational. The number π is an irrational number, because it cannot be expressed as the ratio of two integers (as a simple fraction or ratio). It is a non-terminating, non-repeating decimal (3.1415926...).

π

Irrational. The √2 is an irrational number, because it is the square root of a non-perfect square. In addition, it is a non-terminating, non-repeating decimal and it cannot be expressed as the ratio of two integers (as a simple fraction or ratio).

√2

Rational. The √25 is a rational number, because it is the square root of perfect square (5). In addition, it is a terminating decimal (5.0) and it can be expressed as the ratio of two integers (5/1). 5 can further be classified into the rational number subsets of integers , whole numbers, and natural numbers.

√25

Irrational. The √8 is an irrational number, because it is the square root of a non-perfect square. In addition, it is a non-terminating, non-repeating decimal and it cannot be expressed as the ratio of two integers (as a simple fraction or ratio).

√8