Question

Write two decimals one repeating and one terminating with values between 0 and 1 then write an inequality that shows the relationship between your two decimals

Answer 1

0.111111....... < 0.125

Explanation:

Since, a number defined by,

A = {
`(1)/(n)` : n∈ N} lies between 0 and 1,

That is,

`(1)/(9)` ∈ A,

`(1)/(8)` ∈ A,

Also, in the number line the numbers are arranged in increasing order from left to right,

∵
`(1)/(8)` is right to
`(1)/(9)` in the number line,

`\implies (1)/(9)<(1)/(8)`

`\implies 0.1111.... < 0.125`

Note : We take
`(1)/(9)` because a fraction having numerator 1 and denominator 'multiple of 3' is always non terminating.