Lesson 4Lesson 4

Comparing and Ordering Comparing and Ordering NumbersNumbers

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Rational numbers are numbers that can be Rational numbers are numbers that can be expressed as fractions that are formed expressed as fractions that are formed from integers. For example, 6/7, -3/13, from integers. For example, 6/7, -3/13, and -3/4 are all rational numbers. Rational and -3/4 are all rational numbers. Rational numbers include all decimals with a finite numbers include all decimals with a finite number of digits (0.5, 1.3652, and 4.0007) number of digits (0.5, 1.3652, and 4.0007) or repeating patterns (0.143143143143… or repeating patterns (0.143143143143… and 3.67). The line or “bar” over 67 and 3.67). The line or “bar” over 67 means that the digits 6 and 7 are repeated means that the digits 6 and 7 are repeated indefinitely: 3.67676767…indefinitely: 3.67676767…

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The line or “bar” over 67 means that The line or “bar” over 67 means that the digits 6 and 7 are repeated the digits 6 and 7 are repeated indefinitely: 3.67676767…indefinitely: 3.67676767…

One of the best ways to compare One of the best ways to compare rational numbers is to write them as rational numbers is to write them as decimals.decimals.

Example 1Example 1

Which rational number is greater, 5/6 or Which rational number is greater, 5/6 or 0.833?0.833?

Strategy: Write the fraction as a decimal Strategy: Write the fraction as a decimal and compare the numbers as decimals.and compare the numbers as decimals.

Step 1: Find the decimal equivalence for Step 1: Find the decimal equivalence for 5/6. You can use your calculator if you do 5/6. You can use your calculator if you do not know it. The key sequence is 5 not know it. The key sequence is 5 6 =. 6 =. The solution will be 0.833333…The solution will be 0.833333…

Compare the two decimals.Compare the two decimals.

0.833333. 0.833333. > 0.833, since the digit (3) in the > 0.833, since the digit (3) in the ten thousandths place of 0.833333… is ten thousandths place of 0.833333… is greater than the digit (0) in the ten greater than the digit (0) in the ten thousandths place of 0.833.thousandths place of 0.833.

SolutionSolution

5/6 5/6 > 0.833> 0.833

Example 2Example 2

Place these numbers in order from least to Place these numbers in order from least to greatest: 5 1/3, 5.33, and 5.34.greatest: 5 1/3, 5.33, and 5.34.

Strategy: Compare the numbers as Strategy: Compare the numbers as decimals.decimals.

Step 1: If you don’t know what 1/3 equals Step 1: If you don’t know what 1/3 equals as a decimal use you calculator to find out. as a decimal use you calculator to find out. Write 5 1/3 as a decimal to six places; Write 5 1/3 as a decimal to six places;

5.3333335.333333

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Step 2: Write out 6 places of 5.34; Step 2: Write out 6 places of 5.34; 5.3434345.343434

Step 3: Compare the three numbers. The Step 3: Compare the three numbers. The three numbers all have the same whole three numbers all have the same whole number (5) and the same tenths place (3). number (5) and the same tenths place (3). Two of the numbers, 5 1/3 and 5.33, have Two of the numbers, 5 1/3 and 5.33, have the same digit (3) in the hundredths place, the same digit (3) in the hundredths place, so 5.34 is greater than 5 1/3 and 5.33. so 5.34 is greater than 5 1/3 and 5.33. Comparing the digits in the thousandths Comparing the digits in the thousandths place of 5 1/3 and 5.33 shows that 5.33 is place of 5 1/3 and 5.33 shows that 5.33 is smaller. (5.33 has a 0 in the .001 place).smaller. (5.33 has a 0 in the .001 place).

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SolutionSolution

The order of the numbers from smallest to The order of the numbers from smallest to largest is 5.33, 5 1/3, and 5.34.largest is 5.33, 5 1/3, and 5.34.

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