Problem 307 - Intermediate Algebra

Question

In the following exercises, locate the numbers on a number line. $$ \text { (a) }-1.6 \text { (b) } 3.25 $$

Step-by-Step Solution

Answer

-1.6 is to the left of -1, and 3.25 is slightly past 3.

Step 1: Understand the Number Line

A number line is a straight line with numbers placed at equal intervals or segments along its length. Negative numbers are placed to the left of zero, and positive numbers are placed to the right.

Step 2: Plotting -1.6

Find -1 on the number line. Since -1.6 is 0.6 units to the left of -1, locate the point that is slightly more than halfway between -1 and -2. Mark this point as -1.6.

Step 3: Plotting 3.25

Find 3 on the number line. Since 3.25 is 0.25 units to the right of 3, locate a point that is one-fourth of the distance from 3 to 4. Mark this point as 3.25.

Key Concepts

Locating Numbers

When you are asked to locate numbers on a number line, the first step involves understanding the structure of the number line.
A number line is a straight line where numbers appear in a sequence, divided into equal segments.
On this line, zero is a crucial reference point, with negative numbers placed to the left and positive numbers to the right.
To locate a specific number, you identify its position relative to zero.
Then, you count the units to place the number in its correct spot.

Negative Numbers

Negative numbers are numbers less than zero and appear on the left side of the number line.
An important aspect of negative numbers is understanding their distance from zero.
For example, -1.6 is situated to the left of -1 but not quite at -2.
When you need to plot a negative decimal like -1.6, recognize that it