Chapter 2.7, Problem 1MS

X marks the “X-act” spot.

On the number tine above, place an X on the approximate location for each of the following numbers:

$\frac{3}{2},-\frac{1}{3},2.3,-1.1,0.9,1.05,-\mathrm{0.55.}$

To determine

To mark: The given numbers on number line.

Explanation of Solution

Given information: The given numbers are

  $\frac{3}{2},-\frac{1}{3},2.3,-1.1,0.9,1.05,-0.55$ .

Concept used:

A real number line can be used to mark any real number on it. 0 is located at the middle of the number line. Left side of 0 is used to mark negative numbers, and right side of 0 is used to mark positive numbers. Each interval of consecutive natural numbers are filled with infinite rational and irrational numbers.

Let us construct a number line as shown.

  

The given numbers are

  $\frac{3}{2},-\frac{1}{3},2.3,-1.1,0.9,1.05,-0.55$

Now, express each rational number in decimal form.

  $\begin{array}{l}\frac{3}{2}=1.5\\ -\frac{1}{3}=-\mathrm{0.333..}\end{array}$

  $1.5$ will be located at the middle of 1 and 2, to the right hand side of 0.

  

  $-\mathrm{0.333...}$ will be located to the left side of 0 and near to $0$ .

  

  $2.3$ will be located after 3 point of 2, to the right hand side of 0.

  

  $-1.1$ will be located to the left side of $-1$ and near to $-1$ .

  

  $0.9$ will be located to the right hand side of 0 and it will be near to 1.

  

  $1.05$ will be located, to the right hand side of 1 and it will be very near to 1.

  

  $-0.55$ will be located to the left side of 0, and to the middle position of 0 and $-1$ .