Express the following with appropriate units and significant figures: (a) 1.0 m plus 1

Explain why measurement standards based on laboratory procedures are preferable to those based on specific objects such as the international prototype kilogram.

Which measurement standards are now defined operationally? Which arent?

When a computer that carries seven significant figures adds 1.000000 and 2.5310215, whats its answer? Why?

Why doesnt Earths rotation provide a suitable time standard?

To raise a power of 10 to another power, you multiply the exponent by the power. Explain why this works.

What facts might a scientist use in estimating Earths age?

How would you determine the length of a curved line?

Write 1/x as x to some power.

Emissions of carbon dioxide from fossil-fuel combustion are often expressed in gigatonnes per year, where But sometimes emissions are given in petagrams per year. How are the two units related? 1

The power output of a typical large power plant is 1000 megawatts (MW). Express this result in (a) W, (b) kW, and (c) GW. 1

The diameter of a hydrogen atom is about 0.1 nm, and the diameter of a proton is about 1 fm. How many times bigger than a proton is a hydrogen atom? 1

Use the definition of the meter to determine how far light travels in 1 ns. 1

In nanoseconds, how long is the period of the cesium-133 radiation used to define the second? 1

Lake Baikal in Siberia holds the worlds largest quantity of fresh water, about 14 Eg. How many kilograms is that? 1

A hydrogen atom is about 0.1 nm in diameter. How many hydrogen atoms lined up side by side would make a line 1 cm long? 1

How long a piece of wire would you need to form a circular arc subtending an angle of 1.4 rad, if the radius of the arc is 8.1 cm? 1

Making a turn, a jetliner flies 2.1 km on a circular path of radius 3.4 km. Through what angle does it turn? 1

A car is moving at 35.0 mi/h. Express its speed in (a) m/s and (b) ft/s. 1

You have postage for a 1-oz letter but only a metric scale. Whats the maximum mass your letter can have, in grams? 2

A year is very nearly By what percentage is this figure in error? 2

How many cubic centimeters are in a cubic meter? 2

Since the start of the industrial era, humankind has emitted about half an exagram of carbon to the atmosphere. Whats that in tonnes 2

A gallon of paint covers Whats its coverage in 2

Highways in Canada have speed limits of 100 km/h. How does this compare with the 65 mi/h speed limit common in the United States? 2

One m/s is how many km/h?

A 3.0-lb box of grass seed will seed of lawn. Express this coverage in 2

A radian is how many degrees? Section 1.3 Working with Numbers 2

Add 3.63105 m and 2.13103 km. 2

Divide 4.23103 m/s by 0.57 ms, and express your answer in 3

Add 5.131022 cm and 6.83103 mm, and multiply the result by 1.83104 N (N is the SI unit of force). 3

Find the cube root of without a calculator. 3

Add 1.46 m and 2.3 cm. 3

Youre asked to specify the length of an updated aircraft model for a sales brochure. The original plane was 41 m long; the new model has a 3.6-cm-long radio antenna added to its nose. What length do you put in the brochure? 3

Repeat the preceding exercise, this time using 41.05 m as the airplanes original length. 3

To see why its important to carry more digits in intermediate calculations, determine to three significant figures in two ways: (a) Find and round to three significant figures, then cube and again round; and (b) find to four significant figures, then cube and round to three significant figures. 3

Youve been hired as an environmental watchdog for a big-city newspaper. Youre asked to estimate the number of trees that go into one days printing, given that half the newsprint comes from recycling, the rest from new wood pulp. What do you report? 3

The average dairy cow produces about of milk per year. Estimate the number of dairy cows needed to keep the United States supplied with milk. 3

How many Earths would fit inside the Sun? 3

The average American uses electrical energy at the rate of about 1.5 kilowatts (kW). Solar energy reaches Earths surface at an average rate of about 300 watts on every square meter. What fraction of the United States land area would have to be covered with 20% efficient solar cells to provide all of our electrical energy? 4

Youre writing a biography of the famous physicist Enrico Fermi, who was fond of estimation problems. Heres one problem Fermi posed: Whats the number of piano tuners in Chicago? Give your estimate, and explain to your readers how you got it. 4

(a) Estimate the volume of water going over Niagara Falls each second. (b) The falls provides the outlet for Lake Erie; if the falls were shut off, estimate how long it would take Lake Erie to rise 1 m. 4

Estimate the number of air molecules in your dorm room. 4

A human hair is about 100 m across. Estimate the number of hairs in a typical braid. 4

Youre working in the fraud protection division of a credit-card company, and youre asked to estimate the chances that a 16-digit number chosen at random will be a valid credit-card number. What do you answer? 4

Bubble gums density is about You blow an 8-g wad of gum into a bubble 10 cm in diameter. Whats the bubbles thickness? (Hint: Think about spreading the bubble into a flat sheet. The surface area of a sphere is ) 4

The Moon barely covers the Sun during a solar eclipse. Given that Moon and Sun are, respectively, and from Earth, determine how much bigger the Suns diameter is than the Moons. If the Moons radius is 1800 km, how big is the Sun? 4

The semiconductor chip at the heart of a personal computer is a square 4 mm on a side and contains electronic components. (a) Whats the size of each component, assuming theyre square? (b) If a calculation requires that electrical impulses traverse components on the chip, each a million times, how many such calculations can the computer perform each second? (Hint: The maximum speed of an electrical impulse is close to the speed of light.) 4

Estimate the number of (a) atoms and (b) cells in your body. 4

When we write the number 3.6 as typical of a number with two significant figures, were saying that the actual value is closer to 3.6 than to 3.5 or 3.7; that is, the actual value lies between 3.55 and 3.6 Show that the percent uncertainty implied by such twosignificant- figure precision varies with the value of the number, being the lowest for numbers beginning with 9 and the highest for numbers beginning with In particular, what is the percent uncertainty implied by the numbers (a) 1.1, (b) 5.0, and (c) 9.9? 5 In particular, what is the percent uncertainty implied by the numbers (a) 1.1, (b) 5.0, and (c) 9.9? 5

Continental drift occurs at about the rate your fingernails grow. Estimate the age of the Atlantic Ocean, given that the eastern and western hemispheres have been drifting apart. 5

Youre driving into Canada and trying to decide whether to fill your gas tank before or after crossing the border. Gas in the United States costs $2.97/gallon, in Canada its 94/L, and the Canadian dollar is worth 87 in U.S. currency. Where should you fill up? 5

In the 1908 London Olympics, the intended 26-mile marathon was extended 385 yards to put the end in front of the royal reviewing stand. This distance subsequently became standard. Whats the marathon distance in kilometers, to the nearest meter? 5

Express the following with appropriate units and significant figures: (a) 1.0 m plus 1 mm, (b) 1.0 m times 1 mm, (c) 1.0 m minus 999 mm, (d) 1.0 m divided by 999 mm. 5

Youre shopping for a new computer, and a salesperson claims the microprocessor chip in the model youre looking at contains 33108 m/s, 104 109 10 billion electronic components. The chip measures 5 mm on a side and uses 32-nm technology, meaning each component is 32 nm across. Is the salesperson right? 5

Caf Milagro sells coffee online. A half-kilogram bag of coffee costs $8.95, excluding shipping. If you order six bags, the shipping costs $6.9 Whats the cost per bag when you include shipping? 5

The world consumes energy at the rate of about 450 EJ per year, where the joule (J) is the SI energy unit. Convert this figure to watts (W), where and then estimate the average per capita energy consumption rate in watts. The human body contains about cells, and the diameter of a typical cell is about 10 Like all ordinary matter, cells are made of atoms; a typical atomic diameter is 0.1 nm. 5

How does the number of atoms in a cell compare with the number of cells in the body? a. greater b. smaller c. about the same 5

The volume of a cell is about a. b. c. d. 5

The mass of a cell is about a. b. c. d. 6

The number of atoms in the body is closest to