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Plot Real Numbers Solutions

• Any real number can be represented on a    number line   .
• A number line extends to    positive infinity    on the right and to    negative infinity    on the left, indicated by arrows on each side of the number line.
•    Zero    separates negative and positive numbers.

• Between each integer on the number line there are    infinitely many    points.
• The    scale    of a number line is what it is counting by, or the distance between two tick marks.
• If a number is not an integer, find the    decimal    equivalent, or an approximation by using technology, to plot the point accurately.
• Rational numbers can be plotted    exactly    by changing the scale of the number line.
• Irrational numbers must be    estimated    to be plotted on a number line because there is no equivalent exact decimal.
• Find the decimal approximation of the irrational number using technology to    compare    irrational and rational numbers.
• Because an irrational number    cannot equal    a rational number, it will either be    greater than    or    less than    the rational number.

Example 1

Plot and label the rational numbers on a number line. Label with the original form of the number.

$–\frac{5}{4},\frac{ 7 }{2}, 250\%, –\frac{12}{3}$

Example 2

Plot and label the real numbers on a number line. Label with the original form of the number. 

$–\sqrt{1}, \pi , 5, –\sqrt{10}$

$–\sqrt{1}=–1, \pi \approx 3.14, –\sqrt{10}\approx –3.16$

Example 3

Compare the rational and irrational numbers using greater than or less than. 

Note

Q: Can an irrational number equal a rational number?

A: No. Irrational numbers are non-terminating and non-repeating. Rational numbers terminate or repeat.