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Lesson 4 Comparing and Ordering Numbers Comparing and Ordering Numbers __

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

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The line or “bar” over 67 means that the digits 6 and 7 are repeated indefinitely: 3.67676767… One of the best ways to compare rational numbers is to write them as decimals.

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Example 1 Which rational number is greater, 5/6 or 0.833? Strategy: Write the fraction as a decimal and compare the numbers as decimals. Step 1: Find the decimal equivalence for 5/6. You can use your calculator if you do not know it. The key sequence is 5 6 =. The solution will be 0.833333…

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

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Solution 5/6 > 0.833

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Example 2 Place these numbers in order from least to greatest: 5 1/3, 5.33, and 5.34. Strategy: Compare the numbers as decimals. Step 1: If you don’t know what 1/3 equals as a decimal use you calculator to find out. Write 5 1/3 as a decimal to six places; 5.333333 5.333333 ____

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Step 2: Write out 6 places of 5.34; 5.343434 Step 3: Compare the three numbers. The three numbers all have the same whole number (5) and the same tenths place (3). Two of the numbers, 5 1/3 and 5.33, have the same digit (3) in the hundredths place, so 5.34 is greater than 5 1/3 and 5.33. Comparing the digits in the thousandths place of 5 1/3 and 5.33 shows that 5.33 is smaller. (5.33 has a 0 in the.001 place). ____

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

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