Question

To which subset of the real number system does the number LaTeX: 1.\overline{5}1. 5 ¯ belong?

Answer 1

The subset of rational numbers

Explanation:

Rational numbers are numbers that can be expressed in the form a/b where ad b are integers. The number
`1.\overline5` is a number with a recurring decimal of 5 and every recurring decimal can be expressed in the form a/b where a and b are both integers therefore, every number with recurring decimal is a rational number.

In the question,
`1.\overline5` can be written as follows;

`1.\overline5 = (14)/(9)` or
`1.\overline5 = 1(5)/(9)`.