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Things to Do with Real Numbers at a Glance

Compare Them

When comparing real numbers, it can help to think of the number line. Ah, how fondly we remember it. Our favorite line of all the lines.

The numbers on a number line get bigger as we go further right on the number line, and smaller as we go further left.

All positive numbers are bigger than zero, and all negative numbers are less than zero. Doesn't mean they can't be friends.

Examples
Exercises

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Example 1

Which is smaller: -200 or 5?
Since -200 is to the left of 5 on the number line, we say that -200 is less than 5. This is abbreviated in symbols by -200 < 5.

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Example 2

Which is bigger: the absolute value of -200, or 5?
Remember that the absolute value of a number is the number of steps it takes to reach that number from zero. (You can only take one step at a time. We're very impressed that you can jump all the way from 3 to 7 in a single bound, but you're going to have to pull it back a skosh.) Since \|-200\| = 200, the absolute value of (-200) is greater than 5. As an inequality, that's \|-200\| > 5.

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Example 3

Compare 0 and n in an inequality if n is any positive number.
Either 0 < n or n > 0 will work, since all positive numbers are bigger than 0.

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Exercise 1

Fill in the blank with <, >, or =.

2 __ 3

Exercise 2

Fill in the blank with <, >, or =.

|-4.5| __ -5

Exercise 3

Fill in the blank with <, >, or =.

-3 __ -2

Exercise 4

Fill in the blank with <, >, or =.

|-17.2| __ 17.2

Exercise 5

Fill in the blank with <, >, or =.

-(-π) __ π

Exercise 6

Fill in the blank with <, >, or =.

-4 __ -89

Exercise 7

Suppose n is a negative number and p is a positive number. Fill in the blank with <, >, or =.

n __ p

Exercise 8

Suppose n is a negative number. Fill in the blank with <, >, or =.

n __ 0

Exercise 9

Suppose p is a positive number. Fill in the blank with <, >, or =.

p __ 0

Exercise 10

Suppose p is a positive number. Fill in the blank with <, >, or =.

|p| __ p

Exercise 11

Suppose n is a negative number. Fill in the blank with <, >, or =.

|n| __ n