Chapter 1.1, Problem 36E

(a)

To determine

To state: whether the inequality $1.1>1.\overline{1}$ is true or false.

Answer to Problem 36E

  $1.1>1.\overline{1}$ is false.

Explanation of Solution

Given information:

An inequality as $1.1>1.\overline{1}$ .

Formula used:

For two numbers a and b

  $a>b$ if the digit after decimal places of a is numerically greater than digits after decimal place of b.

Calculation:

Consider the given inequality.

  $1.1>1.\overline{1}$

Now, it is known that $1.\overline{1}=\mathrm{1.111...}$ .

Now, $1.1$ can be written as $1.10$

Further 1 is numerically greater than 0.

So, $\mathrm{1.111...}>1.1$

Hence, the inequality $1.1>1.\overline{1}$ is false.

(b)

To determine

To state: whether the inequality $8\le 8$ is true or false.

Answer to Problem 36E

  $8\le 8$ is false.

Explanation of Solution

Given information:

An inequality as $8\le 8$ .

Concept used:

If two numbers are numerically equal to each other then one cannot be greater or less than the other number.

Calculation:

Consider the given inequality.

  $8\le 8$

It is obvious that 8 is always strictly equal to 8.

So, 8 cannot be less than 8.

Hence, the inequality $8\le 8$ is false.