Question

explain the density of rational numbers with examples
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Answer 1

Answer:

The density property states that between two rational numbers, there is another rational number. For example, is there a rational number between 0 and 1/2 ? ... The rational number between 0 and 1/4 is 1/8 and the rational number between 1/4 and 1/2 is 3/8.

Answer 2

It means that there is a rational number strictly between any pair of distinct real numbers (rational or irrational).

A rational number between 1/2 and 2/3 is

= 1/2 × (1/2 + 2/3)

= 1/2 × [(3 + 4) / 6]

= 1/2 × 7/6

= 7/12

A rational number between 1/2 and 7/12 is

= 1/2 × (1/2 + 7/12)

= 1/2 × [(6 + 7) / 12]

= 1/2 × 13/12

= 13/24