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Magazine Chapter 2: Problem 64
Graph the numbers \(-3,-\frac{2}{3}, 0,2, \frac{7}{2}\) on a number line. Section 1.4
Short Answer
Expert verified
Mark the points -3, -0.67, 0, 2, and 3.5 on the number line.
Step by step solution
01
Understand the Range of Numbers
Identify the smallest and the largest numbers in the given set: o The smallest number is -3o The largest number is \( \frac{7}{2} \) or 3.5.The number line should include all intervals from -3 to 3.5.
02
Draw the Number Line
Draw a horizontal line and mark evenly spaced points representing integers from -4 to 4.
03
Mark the Integer Points
Label the integer points -4, -3, -2, -1, 0, 1, 2, 3, 4 on the number line.
04
Place the First Number (-3)
Locate -3 on the number line and place a point or dot directly above it.
05
Place the Second Number (-\frac{2}{3})
Convert -\( \frac{2}{3} \) to a decimal since it's between -1 and 0. So -\( \frac{2}{3} \) is approximately -0.67. Place a point at -0.67 between -1 and 0.
06
Place the Number Zero (0)
Locate 0 on the number line and place a point or dot directly above it.
07
Place the Fourth Number (2)
Locate 2 on the number line and place a point or dot directly above it.
08
Place the Fifth Number (\frac{7}{2})
Convert \( \frac{7}{2} \) to a decimal which is 3.5. Place a point at 3.5 between 3 and 4.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
graphing numbers
Graphing numbers on a number line is a fundamental skill in mathematics. It involves visualizing the position of numbers, including integers and fractions, on a horizontal line. This helps us understand the relative positions of values and easily compare them.
To graph numbers correctly, follow these simple steps:
To graph numbers correctly, follow these simple steps:
- Identify the range of numbers you need to graph.
- Draw a horizontal line, known as the number line.
- Mark evenly spaced points representing integers and fractions at appropriate places.
number line
A number line is a visual representation of numbers on a straight, horizontal line. The number line includes both positive and negative numbers, as well as zero.
Each point on the line corresponds to a number.
Here are some key points to remember about number lines:
Each point on the line corresponds to a number.
Here are some key points to remember about number lines:
- A number line extends infinitely in both directions.
- Positive numbers are located to the right of zero, while negative numbers are to the left.
- The distance between consecutive integers is consistent.
integers
Integers are whole numbers that can be positive, negative, or zero. They do not include fractions or decimals. For instance:
- Positive integers: 1, 2, 3...
- Negative integers: -1, -2, -3...
- Zero: 0
fractions
Fractions represent parts of a whole number and are written as the quotient of two integers, such as \(\frac{a}{b}\). When graphing fractions on a number line, it is often useful to convert them to decimal form for precision.
Here are some tips for working with fractions on a number line:
Here are some tips for working with fractions on a number line:
- Convert the fraction to a decimal if necessary, for easier placement.
- Locate the position of the fraction between two integers.
- Ensure the distance is proportionate to the size of the fraction.
