ࡱ> -/, bjbjSS 4F11 NNNbbbb$b3ZttttCCCS3U3U3U3U3U3U3$5>8y3NCOCCCy3tt3 C"RtNtS3 CS3 0|,"1t0fVe0?3303 18;8$18N1HCC CCCCCy3y3U CCC3CCCC8CCCCCCCCC : COMPARING AND ORDERING REAL NUMBERS A) Number Line: -1.75 -1.25 1.25 1.75  ( Smaller Larger ( Numbers Numbers  ( ( ( ( ( ( ( ( ( ( ( -3 -2 -1 0 1 2 3 The trickiest part of knowing where to place a negative number on the number line is realizing that the placement of negative numbers seem to be written in the opposite order as the whole numbers. B) Converting a Fraction to a Decimal: Remember, a fraction like  EMBED Equation.3  means 3 ( 4 So if you have a calculator: Press the buttons in this order 3 ( 4 = The number that appears on your calculator screen is the equivalent decimal version of  EMBED Equation.3 , which is 0.75. But if you dont have a calculator: You are stuck converting by using your long division skills. Since we said that  EMBED Equation.3  means 3 ( 4 we can set up a division problem  EMBED Equation.3  This will also result in an answer of 0.75 also. C) Converting a Mixed Fraction to a Mixed Decimal: If you need to covert a mixed fraction such as 5  EMBED Equation.3  to a mixed decimal, the procedure is very similar to converting a simple fraction like  EMBED Equation.3 . Just rewrite the whole number. It never has to be entered in the calculator or be included in your long division problem, because it does not change when you convert to a decimal. 5  EMBED Equation.3  = 5. ? 2) Use your calculator or long division skills to convert only the fractional part of your number to a decimal.  EMBED Equation.3  = .375 Your final answer is the whole number combined with the decimal version of your fraction. SO, the fraction 5  EMBED Equation.3  = 5.375 as a decimal. D) Comparison Symbols: ( means less than means greater than means equal to E) Comparing and Ordering Fractions and Decimals: This is what you need to know to complete your homework properly. 1) When you are asked to compare fractions and decimals using the symbols <, >, = OR if you are asked to order them from least to greatest, the easiest thing to do is change everything to its decimal form and compare/order the numbers this way.  Why should you change to all decimals? I am glad you asked. Because, it is easier to compare/order numbers when they are all in a similar form. ALL DECIMALS or ALL FRACTIONS THAT HAVE COMMON DENOMINATORS. I am requesting you change all the numbers to decimals, instead of fractions. 2) This is how you should compare/order fractions and decimals. a) Example 1: Compare 7.008 and 7  EMBED Equation.3  using <, >, or = . Solution with required work: 7.008 = 7.008 (no need to change this number) 7  EMBED Equation.3  = 7.250 (but this one needs to be changed to a decimal) Since 7.008 is smaller than 7  EMBED Equation.3  in its new decimal form, the final answer is 7.008 ( 7  EMBED Equation.3  Example 2: Order 3. 17, -3 EMBED Equation.3 , and 3 EMBED Equation.3  from least to greatest. Solution with required work: 3.17 = 3.17 (no need to change this number) -3 EMBED Equation.3  = -3.35 (but the other 2 numbers need to become decimals) 3 EMBED Equation.3  = 3.20 Final Order: -3.35, 3.17, 3.20 (using the decimal versions) OR -3 EMBED Equation.3 , 3.17, 3 EMBED Equation.3  (using the original numbers)  A12 A13 #$%(36V U b c ожznbVJV>h<h+=6OJQJh<h<6OJQJh<hZF6OJQJh<h<+6OJQJ jh<6OJQJ jh<6OJQJh<6OJQJ"jhZFOJQJUmHnHuhZFh<+6OJQJhZF6OJQJhZFOJQJ"hZ[h<+5>*CJOJQJaJhZ[h<+CJOJQJaJh?xh<+CJOJQJaJh.AOJQJh<+5OJQJ$%6c 0 1 ! 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