Introduction

In this lesson, we'll learn the symbols used to compare the sizes of numbers.

One important symbol is the greater than symbol " > ." We use this symbol to show that one number is larger than another.

For example, we can write the fact that 2 is larger than 1 as follows:

2 > 1

In words, we'd say " 2 is greater than 1 " or " 2 is larger than 1. "

When using the greater than symbol, the bigger number always goes on the left. The following mnemonic might help you remember this.

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The "Less Than" Symbol

Another important symbol is the less than symbol " < ." We use this symbol to show that one number is smaller than another.

For example, we can write the fact that 3 is smaller than 5 as follows:

3 < 5

In words, we'd say " 3 is less than 5 " or " 3 is smaller than 5. "

When using the less than symbol, the smaller number always goes on the left. The following mnemonic might help you remember this.

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Comparing Numbers With Different Numbers of Digits

When comparing multi-digit whole numbers, we have the following handy rule:

A whole number is greater than another whole number if it has more digits.

For example, 107 has more digits than 25 . Therefore, we can write

107 > 25.

Similarly, 52,546. has fewer digits than 345,752. Therefore, we can write

52,546 < 345,752.

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Example: Comparing Multi-Digit Whole Numbers Using the "Greater Than" Symbol

Which of the following statements are true?

  1. 702 > 1,024
  2. 7,104 > 896
  3. 11,359 > 8,937
EXPLANATION

Remember that " > " means "greater than."

We can compare whole numbers with different numbers of digits by counting the digits. So, let's count the number of digits in each number.

  • Statement I is false. Since \underbrace{702}_{\color{blue}3\,\text{digits}} has fewer digits than \underbrace{1,024}_{\color{blue}4\,\text{digits}} , we conclude that 702 < 1,024.

  • Statement II is true. Since \underbrace{7,104}_{\color{blue}4\,\text{digits}} has more digits than \underbrace{896}_{\color{blue}3\,\text{digits}} , we conclude that 7,104 > 896.

  • Statement III is true. Since \underbrace{11,359}_{\color{blue}5\,\text{digits}} has more digits than \underbrace{8,937}_{\color{blue}4\,\text{digits}} , we conclude that 11,359 > 8,937.

Therefore, the correct answer is "II and III only."

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Practice: Comparing Multi-Digit Whole Numbers Using the "Greater Than" Symbol

What digit could be written in the missing place below to make the statement true?

\[ \fbox{$\phantom{0}$}\,43 > 1,542 \]

a
 The statement is true for any digit.
b
 $2$ only
c
 The statement is never true.
d
 $4$ only
e
 $5$ only
Practice: Comparing Multi-Digit Whole Numbers Using the "Greater Than" Symbol

Which of the following statements are true?

  1. $426 > 46$
  2. $ 3,763 > 438$
  3. $ 5,001 > 25,008$
a
 I and II only
b
 II only
c
 II and III only
d
 III only
e
 I only
Example: Comparing Multi-Digit Whole Numbers Using the "Less Than" Symbol

Which of the following statements are true?

  1. 389 < 87
  2. 2,100 < 58,162
  3. 25,644 < 116,004
EXPLANATION

Remember that " < " means "less than."

We can compare whole numbers with different numbers of digits by counting the digits. So, let's count the number of digits in each number.

  • Statement I is false. Since \underbrace{389}_{\color{blue}3\,\text{digits}} has more digits than \underbrace{87}_{\color{blue}2\,\text{digits}}, we conclude that 389 > 87.

  • Statement II is true. Since \underbrace{2,100}_{\color{blue}4\,\text{digits}} has fewer digits than \underbrace{58,162}_{\color{blue}5\,\text{digits}} , we conclude that 2,100 < 58,162.

  • Statement III is true. Since \underbrace{25,644}_{\color{blue}5\,\text{digits}} has fewer digits than \underbrace{116,004}_{\color{blue}6\,\text{digits}} , we conclude that 25,644 < 116,004.

Therefore, the correct answer is "II and III only."

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Practice: Comparing Multi-Digit Whole Numbers Using the "Less Than" Symbol

What digit could be put in the missing place below to make the statement true?

\[ \fbox{$\phantom{0}$}\,4,605 < 720,143 . \]

a
 The statement is never true.
b
 The statement is true for any digit.
c
 $9$ only
d
 $4$ only
e
 $6$ only
Practice: Comparing Multi-Digit Whole Numbers Using the "Less Than" Symbol

Which of the following statements are true?

  1. $101 < 2,102$
  2. $4,829 < 973$
  3. $ 190 < 18$
a
 I only
b
 II and III only
c
 II only
d
 III only
e
 I and III only
Number Lines

A number line is a line on which each point represents a number. The numbers are written ascending order from left to right, as shown below.



Number lines help to visualize which numbers are greater and which are smaller than a given number.

For example, all numbers to the left of 12 are less than 12. Similarly, all numbers to the right of 12 are greater than 12.


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Example: Comparing Whole Numbers Using Number Lines

The diagram above shows a number line. Which of the following numbers could be placed into the empty box?

  1. 690
  2. 72
  3. 19,730
EXPLANATION

Since the missing number lies to the left of 3,500, it must be less than this number. Therefore, \fbox{[math]\phantom{0000}[/math]} \lt 3,500.

With that in mind, let's examine our numbers in turn.

  • The number 690 satisfies the condition since it has fewer digits than 3,500. \underbrace{690}_{\textrm{[math]\color{blue}3[/math] digits}} \lt \underbrace{3,500}_{\textrm{[math]\color{blue}4[/math] digits}}

  • The number 72 also satisfies the condition since it has fewer digits than 3,500. \underbrace{72}_{\textrm{[math]\color{blue}2[/math] digits}} \lt \underbrace{3,500}_{\textrm{[math]\color{blue}4[/math] digits}}

  • The number 19,730 does not satisfy the condition since it has more digits than 3,500.

Therefore, the correct answer is "I and II only."

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Practice: Comparing Whole Numbers Using Number Lines

The diagram above shows a number line. Which of the following numbers could be placed into the empty box?

  1. $97$
  2. $16,832$
  3. $486$
a
 I and II only
b
 III only
c
 II only
d
 II and III only
e
 I only
Practice: Comparing Whole Numbers Using Number Lines

The diagram above shows a number line. Which of the following numbers could be placed into the empty box?

  1. $4,861$
  2. $9,782$
  3. $231$
a
 I, II, and III
b
 I only
c
 I and II only
d
 III only
e
 II only
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