Problem 91 - Elementary Algebra Within Reach

Question

Plot the numbers on the real number line. $$2,-3$$

Step-by-Step Solution

Answer

The numbers 2 and -3 are plotted on the number line. Two is on the right side of zero, whereas -3 is on the left side.

Step 1: Understand the number line

A number line is a straight line on which every point represents a real number. These real numbers could be either positive, negative, or zero. If we move to the right, the numbers increase whereas, if we move to the left, the numbers decrease. Zero is the middle point on the number line.

Step 2: Plotting the number 2 on the number line

Start from zero (the central point on the number line) and move two points to the right since it's a positive number. Put a dot or mark at the second point on the right side of zero. This represents the number 2.

Step 3: Plotting the number -3 on the number line

Again start from zero, but this time move three points to the left to represent the negative number -3. Put a dot or mark at the third point on the left from zero, this spot represents the number -3.

Key Concepts

Understanding Real Numbers

Real numbers are all the numbers you encounter in everyday life. This includes whole numbers, fractions, and decimals. Real numbers are essentially any number that can be found on the number line, stretching from negative infinity to positive infinity. They are important because:

• They include both rational and irrational numbers.
• They fill all the points on the number line, leaving no gaps.
• They help in understanding measurements, quantities, and values in mathematics.

Zero is a special real number, acting as a neutral point between positives and negatives. Whenever you're dealing with real numbers, visualize them on a number line for better clarity.

Positive and Negative Numbers

Positive and negative numbers are essential to understanding the number line effectively. Positive numbers are greater than zero and are found to the right side of zero on the number line. These numbers increase in value as you move further right.

• Examples: 1, 10, 2.5

Negative numbers, on the other hand, are less than zero and are found to the left. Their value decreases as you move left.

• Examples: -1, -10, -2.5

The concept of positive and negative numbers helps differentiate values in terms of gains or losses, temperatures, and elevations. Remember, moving right increases value, while moving left decreases it.

Plotting Numbers on the Number Line

Plotting numbers on a number line is a visual way to represent real numbers. This involves marking their positions relative to zero. Understanding this process is crucial for solving mathematical problems that involve addition, subtraction, inequalities, and more. Here's how to plot the given numbers 2 and -3:

• To plot 2, locate the zero point on the number line. Move two spaces to the right and place a mark. This spot represents the number 2, a positive number.
• For -3, start again from zero. This time, move three spaces to the left where you will place another mark. This spot represents the number -3, a negative number.

Plotting makes it easier to visualize and comprehend how different numbers relate to each other on the number line.