Comparing and Ordering Rational Numbers

Comparing and Ordering Real Numbers

What is a Rational Number?

• A number that can be made by dividing two integers (an integer is a positive or negative whole number, like -4, 0, 2, etc.).

• Rational numbers include integers, fractions, and most decimals (finite or repeating).

Comparing Rational Numbers

• We compare rational numbers by their order. For example: 1 is less than 3, -10 is less than 2, etc.

• We can see the order of positive and negative numbers on a number line.

• A number is always LESS THAN the number to its RIGHT on the number line.

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Ordering Rational Numbers

​Convert all numbers to

the same form

Order from least to greatest​

Decimal form is usually the easiest to compare​

Comparing Rational Numbers

Learn how to tell which rational numbers are greater, less than, or equal to.

Learn how to order rational numbers from least to greatest.

Multiple Choice

Ascending means...

• least to greatest

• greatest to least

• average

• mean

Multiple Choice

Descending means...

• below zero

• negative

• least to greatest

• greatest to least

Multiple Choice

Which comparison symbol should be placed between the two numbers?
-1.98                 -1.97

• <
• >
• =

Multiple Choice

Which is the least:  0.06 or 0.060

• 0.06
• They are equal.
• 0.060
• Depends on the time of day.

Multiple Choice

Which comparison symbol should be placed between the two numbers?

• <
• > 
• =

Multiple Choice

Which comparison symbol should be placed between the two numbers?

• <
• > 
• =

Multiple Choice

Which number is the smallest?
-3, |-520|, -520, or 3

• -3
• |-520|
• -520
• 3

Multiple Choice

Order from greatest to least: -12, 15, -1, 3, 

• 15, 3, -1, -12
• 15, 3, -12, -1
• -1, -12, 3, 15
• -12, -1, 3, 15

Multiple Choice

Order the following from least to greatest.  
1/2, 2%, 2.1 x 10^-2, 0.20

• 2%, 2.1 x 10^-2, 1/2, 0.20
• 2%, 2.1 x 10^-2, 0.20, 1/2
• 0.20, 1/2, 2%, 2.1 x 10^-2
• 2.1 x 10^-2, 1/2, 0.20, 2%

Multiple Choice

Put the following in descending order.
4.05 x 10¹, 45%, 3/4, 0.075

• 4.05 x 10¹, 45%, 3/4, 0.075
• 3/4, 45%, 0.075, 4.05 x 10¹
• 4.05 x 10¹, 3/4, 45%, 0.075
• 45%, 0.075, 4.05 x 10¹, 3/4