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Chapter 1: Problem 40

Graph each number on a number line. \(5.25,4 \frac{5}{9},-2 \frac{1}{3}, 0,-3 \frac{2}{5}\)

Short Answer

Expert verified
Plot the numbers at 5.25, 4.56, -2.33, 0, and -3.4 on the number line.

Step by step solution

01

Identify the Numbers

List the numbers to be graphed: \(5.25, 4 \frac{5}{9}, -2 \frac{1}{3}, 0, -3 \frac{2}{5}\).
02

Convert Fractions to Decimals

Convert the mixed numbers into decimal form: \(5.25\) remains as it is. Next, \(4 \frac{5}{9} = 4 + \frac{5}{9} = 4 + 0.56 \approx 4.56\). Then, \(-2 \frac{1}{3} = -2 - \frac{1}{3} = -2 - 0.33 \approx -2.33\). Similarly, \(-3 \frac{2}{5} = -3 - \frac{2}{5} = -3 - 0.4 = -3.4\).
03

Draw the Number Line

Draw a horizontal line and mark equal intervals on it. Label these intervals with appropriate values.
04

Plot the Points

Locate each converted decimal number on the number line:- Place \(5.25\) slightly to the right of \(5\).- Place \(4.56\) slightly past the halfway point between \(4.5\) and \(5\).- Place \(-2.33\) slightly before the third division between \(-2\) and \(-3\).- Place \(0\) at the origin.- Place \(-3.4\) slightly past the midpoint between \(-3\) and \(-4\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Converting Fractions to Decimals
When working with fractions and mixed numbers, you often need to convert them into decimals to make graphing on a number line simpler.
To convert a mixed number to a decimal:
  • Separate the whole number part from the fractional part.
  • Convert the fractional part to a decimal.
  • Add the decimal value to the whole number.
For example, in the fraction 4 5/9, you first take the whole number 4, and then you convert the fraction 5/9 into a decimal. To do this, you divide 5 by 9: 5 梅 9 鈮� 0.56. Therefore, 4 5/9 becomes 4 + 0.56 = 4.56. For negative mixed numbers like -2 1/3, the process is similar: -2 is the whole number, and 1/3 converted to decimal is approximately 0.33. So, -2 1/3 becomes -2 - 0.33 鈮� -2.33. Remember, keeping the signs (positive or negative) right is crucial for accurate plotting.
Plotting Points
Plotting numbers on a number line involves several steps to ensure clarity
  • Draw the number line. A horizontal line with equal intervals marked to represent different values.
  • Determine the scale. Choose equal spaces between each number, considering the numbers you need to plot to fit them comfortably on the line.
For instance, when plotting 5.25, find the 5 mark on the number line and move a quarter step to the right.
Similarly, for 4.56, locate 4.5, move slightly more than halfway between 4.5 and 5. With negative numbers like -2.33 and -3.4, locate the negative positions -2 and -3, then move left (because they are negative) by 0.33 and 0.4, respectively. Lastly, plot 0 at the origin. Always ensure the points are plotted with accuracy, reflecting their exact decimal positions.
Number Line
A number line is a fundamental concept in mathematics, representing numbers graphically.
It's a straight line where each point corresponds to a number. Here鈥檚 how to draw a number line and plot points:
  • Draw a straight horizontal line.
  • Mark equal intervals for each unit.
  • Label the intervals according to the numbers you aim to represent.
For this exercise, you may start from -4 to 6 to accommodate all numbers in the list: 5.25, 4.56, -2.33, 0, -3.4.

Interval points don鈥檛 have to be only units; sometimes, you mark them as fractions or decimals for precision (e.g., marking 0.25 between 0 and 1). Accurate labeling helps in correctly plotting and interpreting the points on the number line.

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