Question

Write a rational number in fraction form that is equivalent to -1.\overline{5}

Answer 1

`(-14)/(9)`.

Explanation:

The given number is
`-1.\overline{5}`.

We need to find a rational number in fraction form that is equivalent to given number.

Let
`x=-1.\overline{5}`

`x=-1.555...` ...(1)

Multiply both sides by 10.

`10x=-15.555...` ...(2)

Subtracting (1) from (2), we get

`10x-x=-15.555...-(-1.555...)`

`9x=-14`

Divide both sides by 9.

`x=(-14)/(9)`

Therefore, the required rational number is
`(-14)/(9)`.