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1.2 Rounding & Calculators

1.2 Rounding & Calculators
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  • 1. Electricity Consumption

    Use the graph to estimate the electricity consumption of the United States. Round your answer so it is reasonable for the context. (See Example 1.)

    • Worked-Out Solution

      From the graph, you can estimate that the consumption of electricity in the United States (in 2008) was about 3900 billion kilowatt hours.

      3,900,000,000,000 kilowatt hours

      Download the spreadsheet of data to determine the actual amount of electricity consumed by the United States in 2008. Was your estimate close?

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     _    _      ___      ______    ______   ______   
    | \  / ||   / _ \\   /_   _//  /_   _// |      \\ 
    |  \/  ||  / //\ \\  `-| |,-    -| ||-  |  --  // 
    | .  . || |  ___  ||   | ||     _| ||_  |  --  \\ 
    |_|\/|_|| |_||  |_||   |_||    /_____// |______// 
    `-`  `-`  `-`   `-`    `-`'    `-----`  `------`  
                                                      
    
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  • 2. Comparing Electricity Consumption

    Estimate the total electricity consumption of Japan, Russia, India, and Canada. Is it greater than or less than the electricity consumption of the United States? (See Example 1.)

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       _____   _    _     _  __   _    _    _____    
      / ___// | || | ||  | |/ // | || | || |  __ \\  
      \___ \\ | || | ||  | ' //  | || | || | |  \ || 
      /    // | \\_/ ||  | . \\  | \\_/ || | |__/ || 
     /____//   \____//   |_|\_\\  \____//  |_____//  
    `-----`     `---`    `-` --`   `---`    -----`   
                                                     
    
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  • 3. Electricity Consumption per Person

    In 2008, the population of the United States was about 304 million. Use the graph to estimate the amount of electricity consumed per person. Round your answer so it is reasonable for the context. (See Example 1.)

    • Worked-Out Solution

      To estimate the electricity consumption per person, divide the consumption by the population.

      3,900,000,000,000 kilowatt-hrs divided by 304,000,000 people = 12,829 kilowatt-hours per person

      In 2008, the U.S. electricity consumption was about 13,000 kilowatt-hours per person.

      Calculator Hint:

      When entering numbers like these into a calculator, you can save keystrokes by dividing out the same number of zeros from the numerator and denominator.

      3,900,000  kilowatt-hrs (the ,000,000 is cancelled) divided by 304 people (the ,000,000 is cancelled)

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     _    _    __   __    _  __    _____    _    _   
    | |  | ||  \ \\/ //  | |/ //  |  ___|| | || | || 
    | |/\| ||   \ ` //   | ' //   | ||__   | || | || 
    |  /\  ||    | ||    | . \\   | ||__   | \\_/ || 
    |_// \_||    |_||    |_|\_\\  |_____||  \____//  
    `-`   `-`    `-`'    `-` --`  `-----`    `---`   
                                                     
    
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  • 4. Comparing Electricity Consumption per Person

    In 2008, the population of Canada was about 33 million. Estimate the amount of electricity consumed per person. Which country consumed more electricity per person, Canada or the United States? (See Example 1.)

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               _    _     ____     __   __  __    __  
      ____    | || | ||  |  _ \\   \ \\/ // \ \\ / // 
     |    \\  | || | ||  | |_| ||   \ ` //   \ \/ //  
     | [] ||  | \\_/ ||  | .  //     | ||     \  //   
     |  __//   \____//   |_|\_\\     |_||      \//    
     |_|`-`     `---`    `-` --`     `-`'       `     
     `-`                                              
    
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  • 5. Comparing Refrigerator Costs

    Two refrigerator models and their annual electricity consumptions are shown. Assume the price of electricity is $0.1202 per kilowatt-hour (kWh). (See Example 2.)

    1. Estimate the annual electricity cost of each model.
    2. How much money will you save in electric bills each year if you buy the top-freezer model instead of the side-by-side model?

    • Worked-Out Solution
      1. To estimate the annual electricity cost, multiply the usage by the cost.

        top freezer = 529 kWhr divided by 1 year times $0.1202/1 kWhr = $63.59 per year
      2. You will save about 76 - 64 = $12 a year in electric bills.
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     _____       ___     _    _     _____    __   _   
    |  __ \\    / _ \\  | \  / ||  |  ___|| | || | || 
    | |  \ ||  | / \ || |  \/  ||  | ||__   | '--' || 
    | |__/ ||  | \_/ || | .  . ||  | ||__   | .--. || 
    |_____//    \___//  |_|\/|_||  |_____|| |_|| |_|| 
     -----`     `---`   `-`  `-`   `-----`  `-`  `-`  
                                                      
    
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  • 6. Comparing Refrigerator Costs

    Two refrigerator models and their annual electricity consumptions are shown. Assume the price of electricity is $0.1202 per kilowatt-hour (kWh). A top-freezer model with an ice dispenser consumes 90 kilowatt-hours per year more than the standard top-freezer model. (See Example 2.)

    1. Estimate the annual electricity cost of the top-freezer model with the ice dispenser.
    2. How much does the ice dispenser add to the annual electricity cost of the top-freezer model?

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      ______   __   __    ______   _    _             
     /_   _//  \ \\/ //  /_____// | || | ||     ___   
     `-| |,-    \ ` //   `____ `  | || | ||    /   || 
       | ||      | ||    /___//   | \\_/ ||   | [] || 
       |_||      |_||    `__ `     \____//     \__ || 
       `-`'      `-`'    /_//       `---`       -|_|| 
                         `-`                     `-`  
    
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  • 7. Comparing Refrigerator Costs

    Two refrigerator models and their annual electricity consumptions are shown. Assume the price of electricity is $0.1202 per kilowatt-hour (kWh). Your current refrigerator consumes 700 kilowatt-hours per year and should last about 7 more years. (See Example 2.)

    1. How much will your current refrigerator cost you over the next 7 years?
    2. How much would the top-freezer model cost you over the same time period?
    3. You buy the top-freezer model for $549.99. Will the difference in electricity costs over the next 7 years cover the price of the new refrigerator? Explain.

    • Worked-Out Solution
      1. Your current refrigertor will cost about
        $84.14 per year
        This is about $84.17 x 7 = $590 over the next 7 years.
      2. From Exercise 5, the top-freezer model would cost about

        7 x 64 = $448

        over the next 7 years.

      3. The difference in the costs of electricity during the 7 years is only about $140. By itself, this does not justify getting rid of your current refrigerator and buying a more efficient model. On the other hand, when your current refrigerator quits working in 7 years, it would be good to consider buying the more "planet friendly" model.

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     _____     __   __    ______    _____     _  _   
    |  __ \\   \ \\/ //  /_   _//  |  ___||  | \| || 
    | |  \ ||   \ ` //   `-| |,-   | ||__    |  ' || 
    | |__/ ||    | ||      | ||    | ||__    | .  || 
    |_____//     |_||      |_||    |_____||  |_|\_|| 
     -----`      `-`'      `-`'    `-----`   `-` -`  
                                                     
    
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  • 8. Finding Electric Bill Savings

    Two refrigerator models and their annual electricity consumptions are shown. Assume the price of electricity is $0.1202 per kilowatt-hour (kWh). You own the top-freezer model. Suppose the price of electricity decreases to $0.12 per kilowatt-hour. How much will you save in electric bills each year? (See Example 2.)

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       _____    ______   __   __     ___      ____    
      / ___//  /_   _//  \ \\/ //   / _ \\   |  _ \\  
      \___ \\   -| ||-    \   //   / //\ \\  | |_| || 
      /    //   _| ||_    / . \\  |  ___  || | .  //  
     /____//   /_____//  /_//\_\\ |_||  |_|| |_|\_\\  
    `-----`    `-----`   `-`  --` `-`   `-`  `-` --`  
                                                      
    
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