Question

Plot the value \(1 / 2,125 \%,-8.4,-3 / 2\), and 2 on the real number line.

Short answer

The decimal values of the given numbers are \(1\), \(0.02125\), \(-8.4\), \(-1.5\), and \(2\). After plotting them on the real number line, their positions are at \(1\), slightly to the right of \(0\), between \(-8\) and \(-9\), between \(-1\) and \(-2\), and at \(2\), respectively.

Step-by-step solution

Convert all given values into decimals

To begin, let's first convert all the given values into decimals: 1. \(1\) is already a decimal. 2. \(2.125 \%\) can be converted by dividing by \(100\): \(2.125 \%/100 = 0.02125\). 3. \(-8.4\) is already a decimal. 4. For \(-3 / 2\), we will perform the division: \(-3 \div 2 = -1.5\). 5. \(2\) is already a decimal. After converting, we now have the following decimal values: \(1\), \(0.02125\), \(-8.4\), \(-1.5\), and \(2\).

Plot the decimal values on the real number line

Now that we have all the decimal values, let's proceed with plotting them on the real number line. 1. Draw a horizontal line, which will represent the real number line. 2. Mark a point in the center of the line and label it as \(0\). 3. Since the decimal values range from \(-8.4\) to \(2\), we will mark the numbers from \(-9\) to \(3\) with equal intervals on the number line. 4. Plot the decimal values: a. Locate \(1\) on the number line and mark the point. b. Locate \(0.02125\) on the number line, which is slightly to the right of \(0\). Mark the point. c. Locate \(-8.4\), which is between \(-8\) and \(-9\). Mark the point. d. Locate \(-1.5\) on the number line, which is between \(-1\) and \(-2\). Mark the point. e. Finally, locate \(2\) on the number line and mark the point. The values have now been successfully plotted on the real number line.

Key concepts

Decimal Conversion

When dealing with numbers in various forms, converting them to decimals can make them easier to work with and compare. Decimal conversion involves expressing non-decimal quantities as decimal numbers. Here's how you can handle conversions in different situations:

• **Whole Numbers and Simple Fractions:** These are often already in a decimal form or are straightforward to convert. A whole number like 1 is already a decimal.


• **Percentages:** To convert a percentage to a decimal, you divide by 100. For example, to convert 2.125% to a decimal: \[2.125\% = \frac{2.125}{100} = 0.02125\]


• **Negative Numbers:** These numbers already have a decimal form, but it's important to note the negative sign remains. For instance, -3/2 is converted to its decimal equivalent using division: \[-\frac{3}{2} = -1.5\]

Accurate decimal conversions help in easy plotting and calculations.

Number Line Plotting

Plotting numbers on a real number line is a powerful way to visualize the order and magnitude of numbers. The real number line is a straight line where each point represents a real number.

Start by drawing a horizontal line, marking a central point as zero. When plotting numbers like 1, 0.02125, -8.4, -1.5, and 2:

• Quantify the range: Our range spans from -9 to 3 to comfortably include all the values.
• Use equal intervals to mark integer numbers clearly on the line.
• Locate and mark decimals between nearest integers. For example, 0.02125 is barely past zero.
• Plot negative numbers to the left of zero, like -8.4 which is between -8 and -9.

Visual representation on a number line helps grasp the relative size and position of numbers.

Negative Numbers

Negative numbers are fascinating as they represent values less than zero and are located on the left side of a number line. Handling negative numbers involves understanding their positions and how operations affect them.

When plotting, remember:

• Numbers to the left are smaller than those to the right.
• -8.4, for instance, is notably left of -1.5 because it has a greater negative magnitude.
• On a number line, these numbers descend further from zero, portraying a reduction in value.

Engaging with negative numbers on a number line can clarify subtraction, debts in modeling, and relative changes in mathematical contexts.

Percentage Conversion

Percentage conversion involves a crucial transformation in mathematics, where we change percentages into decimals, streamlining calculations and comparisons. This conversion is essential in numerical problem solving.

For example, converting a percentage like 2.125% involves dividing it by 100. The reason for this is simple: 'percent' means 'per hundred', effectively making the percentage conversion:
\[2.125\% = \frac{2.125}{100} = 0.02125\]

• This method standardizes numbers, reducing complex problems into simpler, unified decimal forms.
• It also allows for easier addition, subtraction, and visualization, like plotting on a number line.

Thus, percentage conversion is an indispensable tool in both simple arithmetic and sophisticated data analysis.