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,

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

$\implies 0.1111.... < 0.125$

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

Answer 2

This is a fairly easy question. So I'll break it down and give you a description of the terms.

A repeating decimal (like 1/3, 3.333etc is often written as 3.3 with a dot above the second 3 or a ... or an etc) can be anything you chose, 0.7222etc...., 0.3555etc.... Any number which goes on forever. Your choice! A terminating decimal does not go on forever, like 0.25 or 0.43353. It can be as long as you like but it has to end at some point. 


Inequalities are just a question, which value is bigger? You use a < or > to show the relationship, x<y means x is smaller than y. Same for y>x.

So just choose two numbers, 0.333... and... let's say, 0.72. 0.72 is larger so we write 0.333...<0.72

Done!