Problem 306 - Intermediate Algebra

Question

In the following exercises, locate the numbers on a number line. $$ \text { (a) }-0.9 \text { (b) }-2.75 $$

Step-by-Step Solution

Answer

-0.9 and -2.75 are located on a number line to the left of 0, specifically between -1 and -3.

Step 1: Draw the Number Line

Draw a horizontal line and mark the center point as 0. Make sure to include both the positive and negative directions with appropriate equal spacing for the numbers.

Step 2: Locate -0.9 on the Number Line

Starting from 0, move towards the left (negative direction) and find the point that is 0.9 units away from 0. This point is between -1 and 0.

Step 3: Mark -0.9 on the Number Line

Put a point on the number line at the position that corresponds to -0.9, label this point as -0.9.

Step 4: Locate -2.75 on the Number Line

Starting from 0, move further to the left past -1 and -2 until you reach a point that is 2.75 units away from 0. This point will be between -3 and -2.

Step 5: Mark -2.75 on the Number Line

Put a point on the number line at the position that corresponds to -2.75, label this point as -2.75.

Key Concepts

locating numbers

Locating numbers on a number line is an important skill in math. It helps us visualize where numbers are in relation to each other. This is especially helpful for understanding the value and order of numbers.

A number line is a straight, horizontal line. From the center, moving to the right represents the positive direction. Moving to the left represents the negative direction. Here's a step-by-step guide on how to locate a number:

• First, draw a straight, horizontal line.
• Mark the center as 0.
• Place equally spaced marks for positive and negative numbers.

To locate -0.9, start from 0 and move left, 0.9 units past 0. To locate -2.75, start from 0 and move left, 2.75 units past 0. Mark the points and label them accordingly.

negative numbers

Negative numbers are numbers less than zero. They are found to the left of zero on a number line. They represent values below zero, used in various math contexts. Here's how to understand them better:

• Negative sign (-) indicates the number is less than zero.
• Examples are -1, -2, -0.5, -3.14.
• Compare them by looking at their distance from zero: -1 is greater than -2.

When locating negative numbers, always move to the left from zero. The further left you go, the smaller the number's value. Therefore, -2.75 is to the left of -0.9 because it is a smaller number.

step-by-step solutions

Following a step-by-step solution can make finding answers easier. It helps break down complex problems into manageable parts. Here is a quick review of our step-by-step process for locating numbers on a number line:

• Step 1: Draw the number line.
• Step 2: Mark the center as 0.
• Step 3: Place marks for positive and negative values.
• Step 4: Locate -0.9 by moving 0.9 units to the left of 0.
• Step 5: Locate -2.75 by moving 2.75 units to the left of 0.

This detailed step-by-step approach ensures accurate and clear understanding. Following these steps, enables clear visualization of where numbers lie.

intermediate algebra

In intermediate algebra, understanding the number line and negative numbers is crucial. These concepts form the foundation for more advanced topics. Here are some key points:

• Number lines help in visualizing and comparing numbers.
• Negative numbers extend our ability to describe values less than zero.
• Accurately locating numbers is vital for solving algebra problems.

Mastering these concepts allows progressing to more complex equations and functions. Practice with number lines and negative numbers will strengthen this foundation. For example, plotting numbers like -0.9 and -2.75 helps develop a deeper understanding. This lays the groundwork for advanced topics in algebra.