**Rational Numbers:**

Rational numbers are numbers that can be expressed as the quotient or fraction of two integers. In other words, they can be written in the form p/q, where p and q are integers and q is not equal to zero.

To find five rational numbers between two given numbers, we can use the formula:

Rational Number = (a + b) / 2

where 'a' and 'b' are the given numbers. By applying this formula, we can find five rational numbers between any two given numbers.

Let's find five rational numbers between each set of given numbers:

**(i) -1 and 0:**

Using the formula, we can find five rational numbers between -1 and 0:

Rational Number 1 = (-1 + 0) / 2 = -0.5
Rational Number 2 = (-0.5 + 0) / 2 = -0.25
Rational Number 3 = (-0.25 + 0) / 2 = -0.125
Rational Number 4 = (-0.125 + 0) / 2 = -0.0625
Rational Number 5 = (-0.0625 + 0) / 2 = -0.03125

So, the five rational numbers between -1 and 0 are -0.5, -0.25, -0.125, -0.0625, and -0.03125.

**(ii) -2 and -1:**

Using the formula, we can find five rational numbers between -2 and -1:

Rational Number 1 = (-2 + -1) / 2 = -1.5
Rational Number 2 = (-1.5 + -1) / 2 = -1.25
Rational Number 3 = (-1.25 + -1) / 2 = -1.125
Rational Number 4 = (-1.125 + -1) / 2 = -1.0625
Rational Number 5 = (-1.0625 + -1) / 2 = -1.03125

So, the five rational numbers between -2 and -1 are -1.5, -1.25, -1.125, -1.0625, and -1.03125.

**(iii) −45 and −23:**

Using the formula, we can find five rational numbers between -45 and -23:

Rational Number 1 = (-45 + -23) / 2 = -34
Rational Number 2 = (-34 + -23) / 2 = -28.5
Rational Number 3 = (-28.5 + -23) / 2 = -25.75
Rational Number 4 = (-25.75 + -23) / 2 = -24.375
Rational Number 5 = (-24.375 + -23) / 2 = -23.6875

So, the five rational numbers between -45 and -23 are -34, -28.5, -25.75, -24.375, and -23.6875.

**(iv) 12 and 23:**

Using the formula, we can find five rational numbers between 12 and 23:

Rational Number 1 =