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

Answer:

0.111111....... < 0.125

Step-by-step explanation:

Since, a number defined by,

A = {$\frac{1}{n}$ : n∈ N} lies between 0 and 1,

That is,

$\frac{1}{9}$ ∈ A,

$\frac{1}{8}$ ∈ A,

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

∵ $\frac{1}{8}$ is right to $\frac{1}{9}$ in the number line,

$\implies \frac{1}{9}<\frac{1}{8}$

$\implies 0.1111.... < 0.125$

Note : We take $\frac{1}{9}$ because a fraction having numerator 1 and denominator 'multiple of 3' is always non terminating.