Lesson 4 Comparing and Ordering Numbers Comparing and Ordering Numbers __

 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, , and ) or repeating patterns ( … and 3.67). The line or “bar” over 67 means that the digits 6 and 7 are repeated indefinitely: … ____

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

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 …

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

Solution 5/6 > 0.833

Example 2 Place these numbers in order from least to greatest: 5 1/3, 5.33, and 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; ____

Step 2: Write out 6 places of 5.34; 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 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). ____

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