Three of the numbers are rational and can be graphed precisely.
Graph:
Least to greatest:
{- 3 34, - 3.5, - sqrt(10), - 15/5 }
In this set of numbers, we have been given both rational and irrational values. Let's consider these types of numbers individually first.
The Rational Numbers
The numbers - 155, - 3.5 , and - 3 34 are all rational numbers, and they can be written in the form ab. We can rewrite the first number to make drawing our number line easier.
- 15/5= -3
To graph these numbers we can draw a number line from -4 to -3 and divide the segment into four equal spaces. Since - 3 is an integer, we can plot it immediately.
To graph - 3.5, we place a point right in the middle of - 4 and - 3.
To graph - 3 34, we will move one space to the right of - 4.
The Irrational Numbers
The final number is an irrational number, so it cannot be written as a fraction. Using a calculator, we can find an approximate value of the square root. Notice that it is also between - 4 and - 3.
- sqrt(10)=- 3.162277...
This number is between - 3.1 and - 3.2. If we divide the line segment between -4 and -3 into ten equal parts, we can approximate the placement of this value.
Least to Greatest
Now we have graphed each number on the number line, we can write them in order from least to greatest. Lesser numbers are found on the left and greater numbers are on the right. This gives us the following order.
{- 3 34, - 3.5, - sqrt(10), - 155 }
