Unit 3B

Unit 3B

Putting Numbers Into Perspective

Scale of the Universe 2

http://sciencenetlinks.com/tools/scale-universe-2/

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15. Convert each of the following numbers from scientific to ordinary notation, and write its name.

Example:  

 $2\times10^3=2,000$  two thousand

a.  $6\times10^4$  

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15. Convert each of the following numbers from scientific to ordinary notation, and write its name.

Example:  

 $2\times10^3=2,000$  two thousand

b.  $3\times10^5$  

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15. Convert each of the following numbers from scientific to ordinary notation, and write its name.

Example:  

 $2\times10^3=2,000$  two thousand

c.  $3.4\times10^5$  

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15. Convert each of the following numbers from scientific to ordinary notation, and write its name.

Example:  

 $2\times10^3=2,000$  two thousand

d.  $2\times10^{-3}$  

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15. Convert each of the following numbers from scientific to ordinary notation, and write its name.

Example:  

 $2\times10^3=2,000$  two thousand

e.  $6.7\times10^{-2}$  

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15. Convert each of the following numbers from scientific to ordinary notation, and write its name.

Example:  

 $2\times10^3=2,000$  two thousand

f.  $3\times10^{-6}$  

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23–26: Using Scientific Notation. Rewrite the following statements using a number in scientific notation. (Ex: 2,400,000 = 2.4 x 10^6)

23. My hard drive has a capacity of 1.2 terabytes. (Recall that tera- means “trillion.”)

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23–26: Using Scientific Notation. Rewrite the following statements using a number in scientific notation. (Ex: 2,400,000 = 2.4 x 10^6)

25. The diameter of a typical atom is about 0.5 nanometer. (Recall that nano- means “billionth.”)

Open Ended

29–32: Perspective Through Estimation. Use estimation to make the following comparisons. Discuss your conclusion.

32. Which is greater: the amount you spend in a year on transportation or the amount you spend in a year on food?

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39–46: Energy Comparisons. Use Table 3.1 to answer the following questions.

39. How many average candy bars would you have to eat to ­supply the energy needed for 8 hours of running?

39. How many average candy bars would you have to eat to ­supply the energy needed for 8 hours of running?

•  $\frac{1\ candy\ bar}{1\ \times10^6\ joules}$  

•  $\frac{1\ hour\ of\ running}{4\ \times10^6\ joules}$  

•  $\frac{1\ candy\ bar}{1\ \times10^6\ joules}\cdot\frac{4\times10^6\ joules}{1\ hour\ run}=\frac{4\ candy\ bars}{\text{1 hour run}}$  

•  $\frac{4\ candy\ bar}{1\ hour\ run}\cdot\ 8\ hours\ run\ =\ 32\ candy\ bars$  

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39–46: Energy Comparisons. Use Table 3.1 to answer the following questions.

40. How many liters of oil are required to supply the electrical energy needs of an average home for a year?

(Round to the tens place.)

40. How many liters of oil are required to supply the electrical energy needs of an average home for a year?

•  $\frac{1\ liter\ of\ oil}{1.2\times10^7\ joules}\cdot\frac{5\times10^7joules}{1\ house\ \left(daily\right)}$  

•  $\frac{5\ liters\ of\ oil}{1.2\ houses\ \left(daily\right)}=4.16666666\ liters\ per\ house\ daily$  

• 4.16666 liters per day x 365 days = 1520.83 liters

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39–46: Energy Comparisons. Use Table 3.1 to answer the following questions.

43. If you could generate energy by fusing the hydrogen in water, how much water would you need to generate the electrical energy used daily by 10,000 typical homes? (Round to the nearest thousandths.)

43. If you could generate energy by fusing the hydrogen in water, how much water would you need to generate the electrical energy used daily by 10,000 typical homes? (Round to the nearest thousandths.)

•  $\frac{5\times10^7\ joules}{1\ house}\cdot10,000\ house=5\times10^{11}\ joules\ needed$  

•  $5\times10^{11}\ joules\ \cdot\frac{1\ liter\ of\ water}{6.9\times10^{13}\ joules}$  

•  $\frac{5}{6.9}\cdot10^{11-13}\ joules\ =0.724\times10^{-2}\ joules$  

• 0.007 joules

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55. There were approximately 2.69 million deaths in the United States in 2015. Express this quantity in deaths per minute.

55. There were approximately 2.69 million deaths in the United States in 2015. Express this quantity in deaths per minute.

•  $\frac{2,690,000\ deaths}{1\ year}\cdot\frac{1\ years}{365\ days}\cdot\frac{1\ day}{24\ hours}\cdot\frac{1\ hour}{60\ \min}\approx5.11796\ deaths\ per\ \min$  

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63. Cells in the Human Body. Estimates of the number of cells in the human body vary over an order of magnitude. Indeed, the precise number varies from one individual to another and depends on whether you count bacterial cells. Here is one way to make an estimate.

a. Assume that an average cell has a diameter of 6 micro­meters  ( $6\times10^{-6}$  meter), which means it has a volume of 100 cubic micrometers. How many cells are there in a cubic centimeter?

a. Assume that an average cell has a diameter of 6 micro­meters (6×10^−6  meter), which means it has a volume of 100 cubic micrometers. How many cells are there in a cubic centimeter?

•  $1cm\times1cm\times1cm\times\frac{1\ meter}{10^2\ cm}\times\frac{1\ meter}{10^2\ cm}\times\frac{1\ meter}{10^2\ cm}$  

•  $\frac{1\ meter\times meter\times meter}{10^6}\times\frac{1\ micrometer}{10^{-6}\ meter}\times\frac{1\ micrometer}{10^{-6}\ meter}\times\frac{1\ micrometer}{10^{-6}\ meter}$  

•  $\frac{1\ cubic\ micrometers}{10^{-12}}\times\frac{1\ cell}{100\ cubic\ micrometers}$  

•  $\frac{1}{10^{-10}}\ cells\ =\ 10^{10}\ cells$  

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63. Cells in the Human Body. Estimates of the number of cells in the human body vary over an order of magnitude. Indeed, the precise number varies from one individual to another and depends on whether you count bacterial cells. Here is one way to make an estimate.

b. Estimate the number of cells in a liter, using the fact that a cubic centimeter equals a milliliter. (1 cubic cm is 10^10 cells)

b. Estimate the number of cells in a liter, using the fact that a cubic centimeter equals a milliliter. (1 cubic cm is 10^10 cells)

 $1\ liter\ \times\frac{1,000\ milliliters}{1\ liter}\times\frac{1\ cubic\ centimeter}{1\ milliliter}\times\frac{10^{10}\ cells}{1\ cubic\ centimeter}$  

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63. Cells in the Human Body. Estimates of the number of cells in the human body vary over an order of magnitude. Indeed, the precise number varies from one individual to another and depends on whether you count bacterial cells. Here is one way to make an estimate.

c. Estimate the number of cells in a 70-kilogram (154-pound) person, assuming that the human body is 100% water (actually it is about 60–70% water) and that 1 liter of water weighs 1 kilogram.

c. Estimate the number of cells in a 70-kilogram (154-pound) person, assuming that the human body is 100% water (actually it is about 60–70% water) and that 1 liter of water weighs 1 kilogram.

 $70\ kg\ \times\frac{1\ liter}{1\ kg}\times\frac{10^{13}\ cells}{1\ liter}$  

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65. The Amazing Amazon. An issue of National Geographic contained the following statement:

Dropping less than two inches per mile after emerging from the Andes, the Amazon drains a sixth of the world’s runoff into the ocean. One day’s discharge at its mouth—4.5 trillion gallons—could supply all U.S. households for five months.

Based on this statement, determine how much water an average U.S. household uses each month. Does this answer seem reasonable? Explain any estimates you make. (Assume there are 100 million households.)

4.5 trillion gallons—could supply all U.S. households for five months.(Assume 100 million households.)

4.5 trillion gallons / 5 months = 0.9 trillion gallons per month

 $\frac{900,000,000,000\ gallons}{100,000,000\ houses}=9,000\ gallons\ per\ house$  

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69. Personal Consumption. The Bureau of Economic Analysis ­estimates that in 2015, personal consumption expenditures of Americans totaled $12.3 trillion. The major categories of these expenditures were durable goods ($1.36 trillion; for ­example, cars, furniture, recreational equipment), nondurable goods ($2.66 trillion; for example, food, clothing, fuel), and services ($8.3 trillion; for example, health care, ­education, transportation).

a. What was the approximate annual per capita spending on personal consumption? Assume a population of 321 million. (Nearest dollar.)

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69. Personal Consumption. The Bureau of Economic Analysis ­estimates that in 2015, personal consumption expenditures of Americans totaled $12.3 trillion. The major categories of these expenditures were durable goods ($1.36 trillion; for ­example, cars, furniture, recreational equipment), nondurable goods ($2.66 trillion; for example, food, clothing, fuel), and services ($8.3 trillion; for example, health care, ­education, transportation).

b. What was the approximate daily per capita spending on personal consumption?

(Nearest dollar.) ($38,318 annual)

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69. Personal Consumption. The Bureau of Economic Analysis ­estimates that in 2015, personal consumption expenditures of Americans totaled $12.3 trillion. The major categories of these expenditures were durable goods ($1.36 trillion; for ­example, cars, furniture, recreational equipment), nondurable goods ($2.66 trillion; for example, food, clothing, fuel), and services ($8.3 trillion; for example, health care, ­education, transportation).

c. On average, about what percentage of personal consumption spending was devoted to services? Is this figure consistent with your own spending? (Nearest percent.)

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69. Personal Consumption. The Bureau of Economic Analysis ­estimates that in 2015, personal consumption expenditures of Americans totaled $12.3 trillion. The major categories of these expenditures were durable goods ($1.36 trillion; for ­example, cars, furniture, recreational equipment), nondurable goods ($2.66 trillion; for example, food, clothing, fuel), and services ($8.3 trillion; for example, health care, ­education, transportation).

d. Spending on health care was estimated to be $2.1 trillion. About what percentage of all personal consumption spending was devoted to health care?

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69. Personal Consumption. The Bureau of Economic Analysis ­estimates that in 2015, personal consumption expenditures of Americans totaled $12.3 trillion. The major categories of these expenditures were durable goods ($1.36 trillion; for ­example, cars, furniture, recreational equipment), nondurable goods ($2.66 trillion; for example, food, clothing, fuel), and services ($8.3 trillion; for example, health care, ­education, transportation).

e. In 2000, the total spending on personal consumption was $6.8 trillion, while health care spending was $918 billion. Compare the percentage increase in total spending and health care spending between 2000 and 2015.

Fill in the Blank

69. Personal Consumption. The Bureau of Economic Analysis ­estimates that in 2015, personal consumption expenditures of Americans totaled $12.3 trillion. The major categories of these expenditures were durable goods ($1.36 trillion; for ­example, cars, furniture, recreational equipment), nondurable goods ($2.66 trillion; for example, food, clothing, fuel), and services ($8.3 trillion; for example, health care, ­education, transportation).

e. In 2000, the total spending on personal consumption was $6.8 trillion, while health care spending was $918 billion. Compare the percentage increase in total spending and health care spending between 2000 and 2015.