Chapter 2

Four people listening to a 2800 -word speech counted the number of words in the speech as they were listening. They came up with these results: \(\begin{array}{ll}\text { Fred: } 2736 \text { words } & \text { Wilma: } 2810 \text { words }\end{array}\) Barney: 2792 words Betty: 2734 words (a) Which person was most accurate? (b) Which person was most precise? (c) Would you judge the group's average word count as being accurate or inaccurate? (d) Four other people heard the same speech and came up with the word counts \(2722,2724,2719\), and 2723 . Is this group more or less accurate than the first? Is this group more or less precise than the first? Answer: (a) Barney was most accurate because 2792 is closest to 2800, the actual number of words in the speech. (b) Because each person made only one count, the term precision doesn't apply. (c) The average word count for the group is ( \(2736+2810+2792+2734) / 4=2768\). This is 32 words fewer than the actual word count of 2800 . Because 32 is quite small relative to 2800 , the group's determination is pretty accurate. (d) The average word count for the second group is \((2722+2724+2719+2723) / 4=\) 2722\. This is 78 words fewer than the actual word count, and so the second group is less accurate than the first. As for precision, the first group ranges from a high of 2810 to a low of 2734 (a spread of 76 ), whereas the second group ranges from a high of 2724 to a low of 2719 (a spread of 5 ). The smaller spread makes the second group more precise.

Two students count the grains of uncooked rice in a small cup. Both students repeat this measurement four times, with the following results: \(\begin{array}{ll}\text { Mike: } 256,263,262,266 & \text { Ike: } 250,242,270,278\end{array}\) The actual number of grains is 260 . Which student is more accurate? Which is more precise? Explain your answers.

Two students attempt to measure out a quart of water into a bucket. Jack has a halfquart container, and Jill has a 10-gallon container. Which student will probably be more accurate at putting a quart of water into the bucket? Explain.

Convert \(4.68 \times 10^{-1}\) to standard notation.

Convert \(47.3 \times 10^{-2}\) to standard notation.

Convert \(47.325 \times 10^{3}\) to standard notation.

Write the following mumbers in standard notation. \(0.400 \times 10^{-6}\)

$$ 6.0 \times 10^{3} $$

$$ 27.5 \text { in. } / 2.0 \mathrm{~h}=? $$

$$ 22.0 \text { miles } \times 2.0 \text { miles }=? $$

Suppose you measure the length of a house to be \(60.50 \mathrm{ft}\). How many yards is that? \((1\) yard \(=3 \mathrm{ft})\)

(a) 1222 pounds \(/ 2.0 \mathrm{in} .=?\) (b) 1222 pounds \(/ 2.00 \mathrm{in} .=?\) (c) What do you get when you quadruple \(21.72 \mathrm{~cm} ?\)

\(1555 \mathrm{in} .+0.001 \mathrm{in} .+0.2 \mathrm{in}=?\)

\(1555 \mathrm{~cm}+0.001 \mathrm{~cm}+0.8 \mathrm{~cm}=?\)

\(142 \mathrm{~cm}-0.48 \mathrm{~cm}=?\)

Express the distance \(24,000,000,000 \mathrm{~m} \pm 100\) million \(\mathrm{m}\) using the appropriate Greek prefix.

Express the distance \(4736 \mathrm{~m}\) in kilometers \((1 \mathrm{~km}=1000 \mathrm{~m})\).

[ Express \(0.025 \mathrm{~m}\) in millimeters \((1 \mathrm{~mm}=0.001 \mathrm{~m})\).

How many milliliters are there in \(1.000 \mathrm{~L}\) ?

How many milliliters are there in \(2.500 \mathrm{~L}\) ?

How many milliliters are there in \(246.7 \mathrm{~cm}^{3} ?\)

The temperature outside is \(263.5 \mathrm{~K}\). What is the temperature in degrees Celsius and in degrees Fahrenheit?

Which is denser, a 200 pound block of lead or a \(0.1-\mathrm{g}\) piece of gold?

A cube that is \(10.0 \mathrm{~mm} \times 10.0 \mathrm{~mm} \times 10.0 \mathrm{~mm}\) has a mass of \(4.70 \mathrm{~g}\). What is its density in grams per milliliter?

A small statue that has a mass of \(500.0 \mathrm{~g}\) displaces \(150.5 \mathrm{~mL}\) of water. What is its density in grams per milliliter?

Which of the following can be thought of as conversion factors? (a) \(49.3 \mathrm{~kg}\) (b) \(4.184 \mathrm{j} /{ }^{\circ} \mathrm{C}\) (c) 350 miles \(/ \mathrm{h}\) (d) 12 eggs per dozen (c) 1 dozen grams

Write two conversion factors (two different ratios) to express the fact that there are \(24 \mathrm{~h}\) in a day.

Given a speed of \(600.0\) miles \(/ \mathrm{h}\) and a measured distance of \(50.0\) miles, multiply the conversion factor by the measured distance to make identical units cancel. Calculate the result and include its units.

Given a speed of \(600.0\) miles/h and a measured time of \(50.0 \mathrm{~h}\), multiply the conversion factor by the measured time to make identical units cancel. Calculate the result and include its units.

The density of gold is \(19.3 \mathrm{~g} / \mathrm{cm}^{3}\). What volume in milliliters will \(20.0 \mathrm{~g}\) of gold occupy? (Hint: Don't be fooled. Remember that \(1 \mathrm{~cm}^{3}=1 \mathrm{~mL}\).)

The density of air is \(0.00130 \mathrm{~g} / \mathrm{mL}\). What is the mass in grams of \(500.0 \mathrm{~L}\) of air? What is this mass in kilograms?

The measured density of lead is \(11.4 \mathrm{~g} / \mathrm{mL}\). What volume in milliliters will \(1.50\) pounds of lead occupy? \([1\) pound \(=453.6 \mathrm{~g}]\)

It takes six cups of flour to bake one cake; exactly one cup of flour has a mass of \(120.0 \mathrm{~g}\). If you have \(6955 \mathrm{~g}\) of flour, how many cakes can you bake? (Hint: Two conversion factors are given in this problem. Find them and write them down first in ratio form. Then use them in the correct form with the measured quantity, which is \(6955 \mathrm{~g}\) of flour.)

A floor installer can cover \(250.0 \mathrm{~m}^{2}\) of floor area per hour with floor tiles. How many souare feet per minute can he cover?

Given \(p / q=r\), solve for \(p\).

Given \(p / q=r\), solve for \(q\).

Given \(P+Q=z\), solve for \(P\).

Suppose you have a 2.000-pound block of iron at \(50.0^{\circ} \mathrm{C}\). How much heat in joules would it take to warm this block to \(75.0^{\circ} \mathrm{C}\) ?

\(\mathrm{A} 20.0-\mathrm{g}\) block of iron initially at \(25.0^{\circ} \mathrm{C}\) has \(100.0 \mathrm{~J}\) of heat energy added to it. What is its temperature after the heat energy has been added?

A \(0.100-g\) sample of your favorite candy is burned in a calorimeter that contains \(1.00 \mathrm{~kg}\) of water initially at \(22.0^{\circ} \mathrm{C}\). After the candy is burned, the water temperature is \(35.5^{\circ} \mathrm{C}\). How many Calories are there per gram of your candy?

There are \(3 \mathrm{ft}\) in a yard. A certain piece of wood is \(3 \mathrm{ft}\) long. What is the fundamental difference between the value of \(3 f t\) in these two statements?

Jack is asked to determine the number of pennies in \(\$ 1.00\). Jill is asked to determine the number of liters in 1 gallon. Whose answer will be an exact number, and whose will be measured? Explain why.

Three people measure the distance from Main Street to Market Avenue using their best estimates. Their data are \(2.5\) miles, \(2.5\) miles, and \(2.6\) miles. Survey charts show the actual distance to be \(1.8\) miles. Characterize the collected data in terms of accuracy and precision.

Two people attempt to measure the length in feet of a parking lot they know to be about \(100 \mathrm{ft}\) long. One person uses a 6 -in. ruler; the other uses a 120 -ft tape measure. If both measuring devices are graduated in \(1 / 16\) in., which person is likely to make the more accurate measurement? Explain.

A ruler is marked in intervals of \(1 / 8\) in. To what fraction of an inch can you estimate a measurement?

Is it possible for a measured quantity to have no uncertainty associated with it? Explain.

What is the uncertainty in each measured number: (a) \(12.60 \mathrm{~cm}\) (b) \(12.6 \mathrm{~cm}\) (c) \(0.00000003\) in. (d) \(125 \mathrm{ft}\)

Underline any trailing zeros in these measurements: (a) \(12.202 \mathrm{~km}\) (b) \(0.01 \mathrm{~mL}\) (c) \(205^{\circ} \mathrm{C}\) (d) \(0.010 \mathrm{~g}\)

The measurement \(30 \mathrm{ft}\) is ambiguous, but the measurement \(30 . \mathrm{ft}\) is not. Explain what the ambiguity is, and how adding the decimal point eliminates the ambiguity.

Give all interpretations possible for the measurement \(2200 \mathrm{ft}\).