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1.2 Rounding & Calculators

1.2 Rounding & Calculators
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  • 13. Estimating the Population of Texas

    Rewrite the statement using the number of significant digits that seems appropriate in the context of the statement. Explain your reasoning. (See Example 5.)

    "In 2009, the population of Texas was 24,782,302 people."

    • Worked-Out Solution

      Two possible solutions are:

      "In 2009, the population of Texas was about 25 million."

      or

      "In 2009, the population of Texas was about 24.8 million."

      When making statements about population size, you should remember that counting large populations is difficult. Think about the following.

      • 2009 is 9 years after the 2000 Census and 1 year before the 2010 Census.

      • Claiming to know the exact population in 2009 is unreasonable.

      • The phrase "in 2009" is ambiguous. On which day in the year is the population being measured?

      For these and other reasons, the most honest statement is "In 2009, the population of Texas was about 25 million." This number list 2 significant digits. The results of the 2010 Census are shown below.

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     __   __     ___                _____    _    _   
     \ \\/ //   / _ \\    ____     |  ___|| | || | || 
      \   //   | / \ ||  |    \\   | ||__   | || | || 
      / . \\   | \_/ ||  | [] ||   | ||__   | \\_/ || 
     /_//\_\\   \___//   |  __//   |_____||  \____//  
     `-`  --`   `---`    |_|`-`    `-----`    `---`   
                         `-`                          
    
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  • 14. Estimating the Price of a House

    Rewrite the statement using the number of significant digits that seems appropriate in the context of the statement. Explain your reasoning. (See Example 5.)

    "The price of a house is $239,900."

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     __   _     ______    _____     ______     _____  
    | || | ||  /_   _//  /  ___||  /_   _//   / ___// 
    | '--' ||   -| ||-  | // __     -| ||-    \___ \\ 
    | .--. ||   _| ||_  | \\_\ ||   _| ||_    /    // 
    |_|| |_||  /_____//  \____//   /_____//  /____//  
    `-`  `-`   `-----`    `---`    `-----`  `-----`   
                                                      
    
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  • 15. Estimating the Weight of a Bag of Sugar

    Rewrite the statement using the number of significant digits that seems appropriate in the context of the statement. Explain your reasoning. (See Example 5.)

    "The weight of a bag of sugar is 5.01 pounds."

    • Worked-Out Solution

      Think about the following:

      • It is difficult to imagine a context in which anyone would care about 0.01 pound of sugar. A teaspoon of sugar weighs about 1/6 ounce, which is about 0.01 pound.

      • What is the accuracy of the scale on which the bag was weighed? A typical scale does not have an accuracy that is within 0.01 pound. Of course, it is possible that the bag of sugar was weighed on a very accurate scale and that its weight is exactly 5.01 pounds. Still, this is unlikely.

      A better statement is clearly

      "The weight of a bag of sugar is about 5 pounds."

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     _____     _    _    __   _      ___      _____   
    |  __ \\  | || | || | || | ||   / _ \\   /  ___|| 
    | |  \ || | || | || | '--' ||  | / \ || | // __   
    | |__/ || | \\_/ || | .--. ||  | \_/ || | \\_\ || 
    |_____//   \____//  |_|| |_||   \___//   \____//  
     -----`     `---`   `-`  `-`    `---`     `---`   
                                                      
    
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  • 16. Estimating the Number of Calories in a Sandwich

    Rewrite the statement using the number of significant digits that seems appropriate in the context of the statement. Explain your reasoning. (See Example 5.)

    "The number of calories in a sandwich is 297."

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      _  _    _    _     _____    _    _      _____  
     | \| || | || | ||  /  ___|| | || | ||   / ___// 
     |  ' || | || | || | // __   | || | ||   \___ \\ 
     | .  || | \\_/ || | \\_\ || | \\_/ ||   /    // 
     |_|\_||  \____//   \____//   \____//   /____//  
     `-` -`    `---`     `---`     `---`   `-----`   
                                                     
    
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  • 17. Estimating the Area of a Room

    Use the floor plan. Write your answer with only as many significant digits as you think are reasonable. (See Example 6.)

    You are carpeting the living room.

    1. How many square feet of carpet should you buy?
    2. The cost of the carpet including installation is $3.49 per square foot. How much does it cost to carpet the living room?
    • Worked-Out Solution
      1. The area of the living room is

        The actual area, however, is somewhat irrelevant when buying carpet. Carpet comes in three basic widths, 12 feet, 13.5 feet and 15 feet. When you are buying carpet that is 12 feet wide, you could get by with 25 feet, as shown in the diagram. So, you should buy
      2. At $3.49 per square foot, the cost of 300 square feet is

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                 ___     _    _    _    _     ____    
        ___     / _ \\  | |  | || | || | ||  |  _ \\  
       /   ||  | / \ || | |/\| || | || | ||  | |_| || 
      | [] ||  | \_/ || |  /\  || | \\_/ ||  | .  //  
       \__ ||   \___//  |_// \_||  \____//   |_|\_\\  
        -|_||   `---`   `-`   `-`   `---`    `-` --`  
         `-`                                          
    
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  • 18. Finding the Area of Usable Floor Space

    Use the floor plan. Write your answer with only as many significant digits as you think are reasonable. (See Example 6.)

    You are replacing the linoleum in the kitchen.

    1. How many square feet of linoleum should you buy? Should you include the area of the two counters in your estimate? Explain.
    2. The cost of the linoleum including installation is $1.25 per square foot. How much does it cost to replace the linoleum in the kitchen?
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      _____      ___      ______    _____    _    _   
     |__  //    / _ \\   /_____//  |  ___|| | |  | || 
       / //    | / \ ||  `____ `   | ||__   | |/\| || 
      / //__   | \_/ ||  /___//    | ||__   |  /\  || 
     /_____||   \___//   `__ `     |_____|| |_// \_|| 
     `-----`    `---`    /_//      `-----`  `-`   `-` 
                         `-`                          
    
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