﻿ Chapter Review - Measurements and Calculations

# Measurements and CalculationsChapter Review

Key Terms

· scientific notation (2.1)

· unit (2.2)

· English system (2.2)

· metric system (2.2)

· SI units (2.2)

· volume (2.3)

· mass (2.3)

· significant figures (2.4)

· rounding off (2.5)

· conversion factor (2.6)

· equivalence statement (2.6)

· dimensional analysis (2.6)

· Fahrenheit scale (2.7)

· Celsius scale (2.7)

· Kelvin (absolute) scale (2.7)

· density (2.8)

· specific gravity (2.8)

For Review

· A quantitative observation is called a measurement and consists of a number and a unit.

· Very large or very small numbers are conveniently expressed by using scientific notation.

o The number is expressed as a number between and multiplied by and raised to a power.

· Units provide a scale on which to represent the results of a measurement. There are three commonly used unit systems.

o English

o Metric (uses prefixes to change the size of the unit)

o SI (uses prefixes to change the size of the unit)

· All measurements have some uncertainty, which is reflected by the number of significant figures used to express the number.

· Rules exist for rounding off to the correct number of significant figures in a calculated result.

· We can convert from one system of units to another by a method called dimensional analysis using conversion factors.

· Conversion factors are built from an equivalence statement, which shows the relationship between the units in different systems.

English—Metric and English—English Equivalents

 Length Mass Volume

· There are three commonly used temperature scales: Fahrenheit, Celsius, and Kelvin.

· We can convert among the temperature scales by adjusting the zero point and the size of the unit. Useful equations for conversions are:

o

o

· Density represents the amount of matter present in a given volume:

Active Learning Questions

These questions are designed to be considered by groups of students in class. Often these questions work well for introducing a particular topic in class.

· 1.

a. There are days/year, hours/day, months/year, and minutes/hour. How many minutes are there in one month?

b. There are hours/day, minutes/hour, days/week, and weeks/month. How many minutes are there in one month?

c. Why are these answers different? Which (if either) is more correct and why?

· 2.

You go to a convenience store to buy candy and find the owner to be rather odd. He allows you to buy pieces only in multiples of four, and to buy four, you need . He allows you only to use pennies and dimes. You have a bunch of pennies and dimes, and instead of counting them, you decide to weigh them. You have g of pennies, and each penny weighs an average of g. Each dime weighs an average of g. Each piece of candy weighs an average of g.

a. How many pennies do you have?

b. How many dimes do you need to buy as much candy as possible?

c. How much would all of your dimes weigh?

d. How many pieces of candy could you buy (based on the number of dimes from part b)?

e. How much would this candy weigh?

f. How many pieces of candy could you buy with twice as many dimes?

· 3.

When a marble is dropped into a beaker of water, it sinks to the bottom. Which of the following is the best explanation?

a. The surface area of the marble is not large enough for the marble to be held up by the surface tension of the water.

b. The mass of the marble is greater than that of the water.

c. The marble weighs more than an equivalent volume of the water.

d. The force from dropping the marble breaks the surface tension of the water.

e. The marble has greater mass and volume than the water.

Explain each choice. That is, for choices you did not pick, explain why you feel they are wrong, and justify the choice you did pick.

· 4.

Consider water in each graduated cylinder as shown: You add both samples of water to a beaker. How would you write the number describing the total volume? What limits the precision of this number?

· 5.

What is the numerical value of a conversion factor? Why must this be true?

· 6.

For each of the following numbers, indicate which zeros are significant and explain. Do not merely cite the rule that applies, but explain the rule.

a.

b.

c.

d.

· 7.

Consider the addition of “ ” to “ .” What would a mathematician say the answer is? What would a scientist say? Justify the scientist’s answer, not merely citing the rule, but explaining it.

· 8.

Consider multiplying “ ” by “ .” What would a mathematician say the answer is? What would a scientist say? Justify the scientist’s answer, not merely citing the rule, but explaining it.

· 9.

In lab you report a measured volume of mL of water. Using significant figures as a measure of the error, what range of answers does your reported volume imply? Explain.

· 10.

Sketch two pieces of glassware: one that can measure volume to the thousandths place, and one that can measure volume only to the ones place.

· 11.

Oil floats on water but is “thicker” than water. Why do you think this fact is true?

· 12.

Show how converting numbers to scientific notation can help you decide which digits are significant.

· 13.

You are driving mph and take your eyes off the road “just for a second.” How many feet do you travel in this time?

· 14.

You have a sample of lead and a sample of glass. You drop each in a separate beaker of water. How do the volumes of water that are displaced by the samples compare? Explain.

· 15.

The beakers shown below have different precisions. a. Label the amount of water in each of the three beakers to the correct number of significant figures.

b. Is it possible for each of the three beakers to contain the exact same amount of water? If no, why not? If yes, did you report the volumes as the same in part a? Explain.

c. Suppose you pour the water from these three beakers into one container. What should be the volume in the container reported to the correct number of significant figures?

· 16.

True or false? For any mathematical operation performed on two measurements, the number of significant figures in the answer is the same as the least number of significant figures in either of the measurements. Explain your answer.

· 17.

Complete the following and explain each in your own words: leading zeros are (never/sometimes/always) significant; captive zeros are (never/sometimes/always) significant; and trailing zeros are (never/sometimes/always) significant.

For any statement with an answer of “sometimes,” give examples of when the zero is significant and when it is not, and explain.

· 18.

For each of the following figures, a through d, decide which block is more dense: the orange block, the blue block, or it cannot be determined. Explain your answers. · 19.

For the pin shown below, why is the third digit determined for the length of the pin uncertain? Considering that the third digit is uncertain, explain why the length of the pin is indicated as cm rather than, for example, or cm. · 20.

Why can the length of the pin shown below not be recorded as cm? · 21.

Use the figure below to answer the following questions. a. Derive the relationship between and .

b. If the temperature outside is , what is the temperature in units of ?

c. Convert to units of , , and .

Questions and Problems: 2.1 Scientific Notation

Questions and Problems with answers below also have full solutions in the Student Solutions Guide.

Questions

· 1.

A represents a quantitative observation.

· 2.

Although your textbook lists the rules for converting an ordinary number to scientific notation, oftentimes students remember such rules better if they put them into their own words. Pretend you are helping your 12-year-old niece with her math homework, and write a paragraph explaining to her how to convert the ordinary number to scientific notation.

· 3.

When a large or small number is written in standard scientific notation, the number is expressed as the product of a number between and , multiplied by the appropriate power of . For each of the following numbers, indicate what number between and would be appropriate when expressing the numbers in standard scientific notation.

a.

b.

c.

d.

· 4.

When a large or small number is written in standard scientific notation, the number is expressed as the product of a number between and , multiplied by the appropriate power of . For each of the following numbers, indicate what power of would be appropriate when expressing the numbers in standard scientific notation.

a.

b.

c.

d.

Problems

· 5.

Will the power of have a positive or a negative exponent when each of the following numbers is rewritten in standard scientific notation?

a.

b.

c.

d.

· 6.

Will the power of have a positive, negative, or zero exponent when each of the following numbers is rewritten in standard scientific notation?

a.

b.

c.

d.

· 7.

Express each of the following numbers in standard scientific notation.

a.

b.

c.

d.

e.

f.

· 8.

Rewrite each of the following as an “ordinary” decimal number.

a.

b.

c.

d.

e.

f.

· 9.

By how many places must the decimal point be moved, and in which direction, to convert each of the following to “ordinary” decimal numbers?

a.

b.

c.

d.

e.

f.

· 10.

By how many places must the decimal point be moved, and in which direction, to convert each of the following to standard scientific notation?

a.

b.

c.

d.

e.

f.

· 11.

Write each of the following numbers in standard scientific notation.

a.

b.

c.

d.

e.

f.

· 12.

Write each of the following numbers as “ordinary” decimal numbers.

a.

b.

c.

d.

e.

f.

· 13.

Write each of the following numbers in standard scientific notation.

a.

b.

c.

d.

e.

f.

g.

h.

· 14.

Write each of the following numbers in standard scientific notation.

a.

b.

c.

d.

e.

f.

g.

h.

Questions and Problems: 2.2 Units

Questions and Problems with answers below also have full solutions in the Student Solutions Guide.

Questions

· 15.

What are the fundamental units of mass, length, and temperature in the metric system?

· 16.

Give the metric prefix that corresponds to each of the following:

a.

b.

c.

d.

e.

f.

Questions and Problems: 2.3 Measurements of Length, Volume, and Mass

Questions and Problems with answers below also have full solutions in the Student Solutions Guide.

Questions

Students often have trouble relating measurements in the metric system to the English system they have grown up with. Give the approximate English system equivalents for each of the following metric system descriptions in Exercises 17, 18, 19 and 20.

· 17.

My new kitchen floor will require square meters of linoleum.

· 18.

My recipe for chili requires a -g can of tomato paste.

· 19.

The gas tank in my new car holds liters.

· 20.

I need some -cm-long nails to hang up this picture.

· 21.

The road sign I just passed says “New York City km,” which is about mi.

· 22.

The GPS in my car indicates that I have mi left until I reach my destination. What is this distance in kilometers?

· 23.

The tablecloth on my dining room table is m long, which is cm or about in.

· 24.

Who is taller, a man who is m tall or a woman who is ft in. tall?

· 25.

The fundamental SI unit of length is the meter. However, we often deal with larger or smaller lengths or distances for which multiples or fractions of the fundamental unit are more useful. For each of the following situations, suggest what fraction or multiple of the meter might be the most appropriate measurement.

a. the distance between Chicago and Saint Louis

b. the size of your bedroom

c. the dimensions of this textbook

d. the thickness of a hair

· 26.

Which English unit of length or distance is most comparable in scale to each of the following metric system units for making measurements?

a. a centimeter

b. a meter

c. a kilometer

· 27.

The unit of volume in the metric system is the liter, which consists of milliliters. How many liters or milliliters is each of the following common English system measurements approximately equivalent to?

a. a gallon of gasoline

b. a pint of milk

c. a cup of water

· 28.

Which metric system unit is most appropriate for measuring the length of an insect such as a beetle?

a. meters

b. millimeters

c. megameters

d. kilometers

Questions and Problems: 2.4 Uncertainty in Measurement

Questions and Problems with answers below also have full solutions in the Student Solutions Guide.

Questions

· 29.

When a measuring scale is used properly to the limit of precision, the last significant digit recorded for the measurement is said to be uncertain. Explain.

· 30.

In lab you report a measured volume of mL of water. Using significant figures as a measure of the error, what range of answers does your reported volume imply? Choose the best answer and justify your choice.

a. mL

b. mL

c. mL

d. mL

e. mL

· 31.

For the pin shown in Fig. 2.5, why is the third figure determined for the length of the pin uncertain? Considering that the third figure is uncertain, explain why the length of the pin is indicated as cm rather than, for example, or cm.

· 32.

Why can the length of the pin shown in Fig. 2.5 not be recorded as cm?

Questions and Problems: 2.5 Significant Figures

Questions and Problems with answers below also have full solutions in the Student Solutions Guide.

Questions

· 33.

Indicate the number of significant figures in each of the following:

a.

b.

c.

d.

· 34.

Indicate the number of significant figures implied in each of the following statements:

a. The population of the United States in 2016 was million.

b. One minute is equivalent to seconds.

c. There are kilometers in mile.

d. The average speed for a four-seat helicopter is about mi/h.

e. The Le Mans racetrack is miles in length.

Questions and Problems: Rounding Off Numbers

Questions and Problems with answers below also have full solutions in the Student Solutions Guide.

Questions

· 35.

When we round off a number, if the number to the right of the digit to be rounded is greater than , then we should .

· 36.

In a multiple-step calculation, is it better to round off the numbers to the correct number of significant figures in each step of the calculation or to round off only the final answer? Explain.

· 37.

Round off each of the following numbers to three significant digits, and express the result in standard scientific notation.

a.

b.

c.

d.

· 38.

Round off each of the following numbers to two significant digits, and express the result in standard scientific notation.

a.

b.

c.

d.

· 39.

Round off each of the following numbers to the indicated number of significant digits and write the answer in standard scientific notation.

a. to three significant digits

b. to three significant digits

c. to four significant digits

d. to four significant digits

· 40.

Round off each of the following numbers to the indicated number of significant digits, and write the answer in standard scientific notation.

a. to two digits

b. to five digits

c. to one digit

d. to four digits

Questions and Problems: Determining Significant Figures in Calculations

Questions and Problems with answers below also have full solutions in the Student Solutions Guide.

Questions

· 41.

Consider the calculation indicated below:

Explain why the answer to this calculation should be reported to only two significant digits.

· 42.

The following water measurements are made: mL of water measured with a beaker, mL of water measured with a graduated cylinder, and mL of water measured with a buret. If all of these water samples are then poured together into one container, what total volume of water should be reported? Support your answer.

· 43.

When the calculation is performed, how many significant digits should be reported for the answer? You should not need to perform the calculation.

· 44.

You are asked to determine the perimeter of the cover of your textbook. You measure the length as cm and the width as cm. How many significant figures should you report for the perimeter?

· 45.

When the sum is calculated, to how many decimal places should the answer be reported? You should not need to perform the calculation.

· 46.

How many digits after the decimal point should be reported when the calculation is performed?

Problems

Note: See the Appendix for help in doing mathematical operations with numbers that contain exponents.

· 47.

Evaluate each of the following mathematical expressions, and express the answer to the correct number of significant digits.

a.

b.

c.

d.

· 48.

Evaluate each of the following mathematical expressions, and express the answer to the correct number of significant digits.

a.

b.

c.

d.

· 49.

Without actually performing the calculations indicated, tell to how many significant digits the answer to the calculation should be expressed.

a.

b.

c.

d.

· 50.

Without actually performing the calculations indicated, tell to how many significant digits the answer to the calculation should be expressed.

a.

b.

c.

d.

· 51.

How many significant digits should be used to report the answer to each of the following calculations? Do not perform the calculations.

a.

b.

c.

d.

· 52.

Evaluate each of the following and write the answer to the appropriate number of significant figures.

a.

b.

c.

d.

Questions and Problems: 2.6 Problem Solving and Dimensional Analysis

Questions and Problems with answers below also have full solutions in the Student Solutions Guide.

Questions

· 53.

A represents a ratio based on an equivalence statement between two measurements.

For Exercises 57 and 58, apples cost per pound.

· 54.

How many significant figures are understood for the numbers in the following definition: ?

· 55.

Given that , determine what conversion factor is appropriate to convert yd to miles; to convert mi to yards.

· 56.

Given that exactly, indicate what conversion factor is appropriate to convert in. to centimeters and to convert cm to inches.

· 57.

What conversion factor is appropriate to express the cost of lb of apples?

· 58.

What conversion factor could be used to determine how many pounds of apples could be bought for ?

Problems

Note: Appropriate equivalence statements for various units are found inside the back cover of this book.

· 59.

Perform each of the following conversions, being sure to set up the appropriate conversion factor in each case.

a. in. to centimeters

b. cm to inches

c. ft to miles

d. ft to meters

e. min to seconds

f. cm to meters

g. m to yards

h. oz to pounds

· 60.

Perform each of the following conversions, being sure to set up the appropriate conversion factor in each case.

a. m to yards

b. yd to meters

c. cm to inches

d. in. to centimeters

e. km to miles

f. mi to kilometers

g. m to kilometers

h. km to centimeters

· 61.

Perform each of the following conversions, being sure to set up the appropriate conversion factor in each case.

a. mi to kilometers

b. gal to quarts

c. calories to joules

d. mm Hg to atmospheres

e. atomic mass units to kilograms

f. in. to centimeters

g. qt to fluid ounces

h. yd to meters

· 62.

Perform each of the following conversions, being sure to set up the appropriate conversion factor in each case.

a. g to kilograms

b. kg to grams

c. kg to pounds

d. kg to ounces

e. g to pounds

f. lb to grams

g. oz to grams

h. g to ounces

· 63.

g of carbon contains carbon atoms. What is the mass in grams of carbon atoms?

· 64.

Los Angeles and Honolulu are mi apart. What is this distance in kilometers?

· 65.

The United States has high-speed trains running between Boston and New York capable of speeds up to mi/h. Are these trains faster or slower than the fastest trains in the United Kingdom, which reach speeds of km/h?

· 66.

The radius of an atom is on the order of m. What is this radius in centimeters? in inches? in nanometers?

Questions and Problems: 2.7 Temperature Conversions

Questions and Problems with answers below also have full solutions in the Student Solutions Guide.

Questions

· 67.

The temperature scale used in everyday life in most of the world except the United States is the scale.

· 68.

The point of water is at on the Fahrenheit temperature scale.

· 69.

The normal boiling point of water is , or .

· 70.

The freezing point of water is K.

· 71.

On both the Celsius and Kelvin temperature scales, there are degrees between the normal freezing and boiling points of water.

· 72.

On which temperature scale ( , , or K) does degree represent the smallest change in temperature?

Problems directs you to the Chemistry in Focus feature in the chapter

· 73.

Make the following temperature conversions:

a. to kelvins

b. K to

c. to kelvins

d. K to

· 74.

Carry out the indicated temperature conversions.

a. to kelvins

b. to kelvins

c. to Fahrenheit degrees

d. to Celsius degrees

· 75.

Convert the following Fahrenheit temperatures to Celsius degrees.

a. a chilly morning in early autumn,

b. a hot, dry day in the Arizona desert,

c. the temperature in winter when my car won’t start,

d. the surface of a star,

· 76.

Convert the following Celsius temperatures to Fahrenheit degrees.

a. the boiling temperature of ethyl alcohol,

b. a hot day at the beach on a Greek isle,

c. the lowest possible temperature,

d. the body temperature of a person with hypothermia,

· 77. The “Chemistry in Focus” segment Tiny Thermometers states that the temperature range for the carbon nanotube gallium thermometers is to .

a. What properties of gallium make it useful in a thermometer?

b. Determine the useful temperature range for the gallium thermometer in Fahrenheit units.

· 78.

Perform the indicated temperature conversions.

a. K to

b. to

c. to

Questions and Problems: 2.8 Density

Questions and Problems with answers below also have full solutions in the Student Solutions Guide.

Questions

· 79.

What does the density of a substance represent?

· 80.

The most common units for density are .

· 81.

A kilogram of lead occupies a much smaller volume than a kilogram of water because has a much higher density.

· 82.

If a solid block of glass, with a volume of exactly , is placed in a basin of water that is full to the brim, then of water will overflow from the basin.

· 83.

Is the density of a gaseous substance likely to be larger or smaller than the density of a liquid or solid substance at the same temperature? Why?

· 84.

What property of density makes it useful as an aid in identifying substances?

· 85.

Referring to Table 2.8, which substance listed is most dense? Which substance is least dense? For the two substances you have identified, for which one would a -g sample occupy the larger volume?

· 86.

Referring to Table 2.8, determine whether magnesium, ethanol, silver, or salt is the least dense.

Problems

· 87.

For the masses and volumes indicated, calculate the density in grams per cubic centimeter.

a. ;

b. ;

c. ;

d. ;

· 88.

For the masses and volumes indicated, calculate the density in grams per cubic centimeter.

a. ;

b. ;

c. ;

d. ;

· 89.

The element bromine at room temperature is a liquid with a density of g/mL. Calculate the mass of mL of bromine. What volume does g of bromine occupy?

· 90.

Sunflower oil has a density of g/mL. What is the mass of L of sunflower oil? What volume (in L) would g of sunflower oil occupy?

· 91.

If mL of linseed oil has a mass of g, calculate the density of linseed oil.

· 92.

A material will float on the surface of a liquid if the material has a density less than that of the liquid. Given that the density of water is approximately g/mL under many conditions, will a block of material having a volume of and weighing lb float or sink when placed in a reservoir of water?

· 93.

Iron has a density of . If g of iron is added to mL of water in a graduated cylinder, to what volume reading will the water level in the cylinder rise?

· 94.

You want to make a rectangular box that weighs pounds and floats on water. The width and height of the box are each cm long. Choose the minimum length of the box that will keep it afloat on the water. Assume the density of water is . Show all work, and explain in words why you chose your answer.

a. cm

b. cm

c. cm

d. cm

e. cm

· 95.

Use the information in Table 2.8 to calculate the volume of g of each of the following substances.

a. sodium chloride

b. mercury

c. benzene

d. silver

· 96.

Use the information in Table 2.8 to calculate the mass of of each of the following substances.

a. gold

b. iron

d. aluminum directs you to the Chemistry in Focus feature in the chapter

· 97.

Indicate the number of significant digits in the answer when each of the following expressions is evaluated (you do not have to evaluate the expression).

a.

b.

c.

· 98.

Express each of the following as an “ordinary” decimal number.

a.

b.

c.

d.

e.

f.

g.

h.

· 99.

Write each of the following numbers in standard scientific notation, rounding off the numbers to three significant digits.

a.

b.

c.

d.

e.

· 100.

For the measurement meters, indicate which (if any) zeros are significant and which (if any) are not significant. Account for all five zeros in the measurement, and explain your reasoning.

· 101.

Make the following conversions.

a. in. to feet and to centimeters

b. qt to gallons and to liters

c. ft to miles and to kilometers

d. kg lead to its volume in cubic centimeters

e. mL ethanol to its mass in grams

f. of mercury to its volume in milliliters and its mass in kilograms

· 102.

On the planet Xgnu, the most common units of length are the blim (for long distances) and the kryll (for shorter distances). Because the Xgnuese have fingers, perhaps it is not surprising that .

a. Two cities on Xgnu are blim apart. What is this distance in kryll?

b. The average Xgnuese is kryll tall. What is this height in blims?

c. This book is presently being used at Xgnu University. The area of the cover of this book is square krylls. What is its area in square blims?

· 103.

You pass a road sign saying “New York km.” If you drive at a constant speed of km/h, how long should it take you to reach New York?

· 104.

Which of the following statements is (are) true?

a. A -liter bottle contains more soda than a -quart bottle.

b. A man who is m tall is taller than a woman who is ft in. tall.

c. A -g container of peanut butter is heavier than a container holding pound.

d. A bus moving at a speed of mi/hr is traveling faster than a car moving at km/hr.

· 105.

Suppose your car is rated at mi/gal for highway use and mi/gal for city driving. If you wanted to write your friend in Spain about your car’s mileage, what ratings in kilometers per liter would you report?

· 106.

You are in Paris, and you want to buy some peaches for lunch. The sign in the fruit stand indicates that peaches are euros per kilogram. Given that there are approximately euros to the dollar, calculate what a pound of peaches will cost in dollars.

· 107.

For a pharmacist dispensing pills or capsules, it is often easier to weigh the medication to be dispensed rather than to count the individual pills. If a single antibiotic capsule weighs g, and a pharmacist weighs out g of capsules, how many capsules have been dispensed?

· 108.

On the planet Xgnu, the natives have fingers. On the official Xgnuese temperature scale , the boiling point of water (under an atmospheric pressure similar to earth’s) is , whereas water freezes at . Derive the relationship between and .

· 109.

For a material to float on the surface of water, the material must have a density less than that of water ( g/mL) and must not react with the water or dissolve in it. A spherical ball has a radius of cm and weighs g. Will this ball float or sink when placed in water? (Note: .)

· 110.

A gas cylinder having a volume of L contains g of gas. What is the density of the gas?

· 111.

Using Table 2.8, calculate the volume of g of each of the following:

a. hydrogen gas (at atmosphere pressure)

b. mercury

d. water

· 112.

Ethanol and benzene dissolve in each other. When mL of ethanol is dissolved in L of benzene, what is the mass of the mixture? (See Table 2.8.)

· 113.

When is written in scientific notation, the exponent indicating the power of is .

· 114.

For each of the following numbers, if the number is rewritten in scientific notation, will the exponent of the power of be positive, negative, or zero?

a.

b.

c.

d.

e.

· 115.

For each of the following numbers, if the number is rewritten in scientific notation, will the exponent of the power of be positive, negative, or zero?

a.

b.

c.

d.

· 116.

For each of the following numbers, by how many places does the decimal point have to be moved to express the number in standard scientific notation? In each case, is the exponent positive or negative?

a.

b.

c.

d.

e.

f.

g.

h.

· 117.

For each of the following numbers, by how many places must the decimal point be moved to express the number in standard scientific notation? In each case, will the exponent be positive, negative, or zero?

a.

b.

c.

d.

e.

· 118.

For each of the following numbers, by how many places must the decimal point be moved to express the number in standard scientific notation? In each case, will the exponent be positive, negative, or zero?

a.

b.

c.

d.

e.

· 119.

Express each of the following numbers in scientific (exponential) notation.

a.

b.

c.

d.

e.

f.

g.

h.

· 120.

Express each of the following as an “ordinary” decimal number.

a.

b.

c.

d.

e.

f.

g.

h.

i.

j.

k.

l.

· 121.

Write each of the following numbers in standard scientific notation.

a.

b.

c.

d.

e.

f.

g.

h.

· 122.

Write each of the following numbers in standard scientific notation. See the Appendix if you need help multiplying or dividing numbers with exponents.

a.

b.

c.

d.

e.

f.

g.

h.

· 123.

The fundamental unit of length or distance in the metric system is the .

· 124.

Draw a piece of lab glassware that can appropriately measure the volume of a liquid as mL.

· 125.

Which distance is farther, km or mi?

· 126.

· 127.

The volume L could also be expressed as mL.

· 128.

The distance cm could also be expressed as .

· 129.

Would an automobile moving at a constant speed of km/h violate a -mph speed limit?

· 130.

Which weighs more, g of water or mg of water?

· 131.

Which weighs more, g of gold or mg of gold?

· 132.

The length m can also be expressed as .

· 133.

A perfect cube of unknown elemental composition has a length of m on each side. The mass of the cube is Mg (megagrams). Using this information and Table 2.8, determine the metal used to prepare the cube.

· 134.

You are working on a project where you need the volume of a box. You take the length, height, and width measurements and then multiply the values together to find the volume. You report the volume of the box as . If two of your measurements were m and m, what was the other measurement?

· 135.

Indicate the number of significant figures in each of the following:

a. This book contains over pages.

b. A mile is just over ft.

c. A liter is equivalent to qt.

d. The population of the United States is approaching million.

e. A kilogram is g.

f. The Boeing cruises at around mph.

· 136.

Round off each of the following numbers to three significant digits.

a.

b.

c.

d.

e.

· 137.

Round off each of the following numbers to the indicated number of significant digits.

a. to four digits

b. to three digits

c. to four digits

d. to five digits

· 138.

Evaluate each of the following, and write the answer to the appropriate number of significant figures.

a.

b.

c.

d.

· 139.

Evaluate each of the following, and write the answer to the appropriate number of significant figures.

a.

b.

c.

d.

· 140.

Evaluate each of the following, and write the answer to the appropriate number of significant figures.

a.

b.

c.

d.

· 141.

Given that , determine what conversion factor is appropriate to convert to liters; to convert L to cubic centimeters.

· 142.

A rectangular solid measures m by mm by dm. What is the volume in liters?

· 143.

Perform each of the following conversions, being sure to set up clearly the appropriate conversion factor in each case.

a. cm to millimeters

b. cm to meters

c. nm to centimeters

d. m to kilometers

e. m to kilometers

f. mm to centimeters

g. m to millimeters

h. nm to micrometers

· 144.

Perform each of the following conversions, being sure to set up clearly the appropriate conversion factor(s) in each case.

a. oz to kilograms

b. L to gallons

c. mL to quarts

d. gal to milliliters

e. lb to grams

f. mL to quarts

· 145.

The mean distance from the earth to the sun is mi. What is this distance in kilometers? in centimeters?

· 146.

Given that one metric , how many metric tons are in lb?

· 147.

Convert the following temperatures to kelvins.

a.

b.

c.

d.

e.

f.

· 148.

Carry out the indicated temperature conversions.

a. to kelvins

b. K to Celsius degrees

c. to Celsius degrees

d. to Fahrenheit degrees

· 149.

For the masses and volumes indicated, calculate the density in grams per cubic centimeter.

a. ;

b. ;

c. ;

d. ;

· 150.

A sample of a liquid solvent has a density of g/mL. What is the mass of mL of the liquid?

· 151.

An organic solvent has a density of g/mL. What volume is occupied by g of the liquid?

· 152.

A solid metal sphere has a volume of . The mass of the sphere is lb. Find the density of the metal sphere in grams per cubic centimeter.

· 153.

A sample containing g of metal pellets is poured into a graduated cylinder initially containing mL of water, causing the water level in the cylinder to rise to mL. Calculate the density of the metal.

· 154.

Convert the following temperatures to Fahrenheit degrees.

a.

b. K

c.

d. K

e.

f.

· 155.

For each of the following descriptions, identify the power of being indicated by the prefix in the measurement.

a. The sign on the interstate highway says to tune my AM radio to kilohertz for traffic information.

b. My new digital camera has a -gigabyte flash memory card.

c. The shirt I bought for my dad on my European vacation shows the sleeve length in centimeters.

d. My brother’s camcorder records on -millimeter tape cassettes.

· 156. The “Chemistry in Focus” segment Critical Units! discusses the importance of unit conversions. Read the segment and make the proper unit conversions to answer the following questions.

a. The Mars Climate Orbiter burned up because it dipped lower in the Mars atmosphere than planned. How many miles lower than planned did it dip?

b. A Canadian jetliner almost ran out of fuel because someone pumped less fuel into the aircraft than was thought. How many more pounds of fuel should have been pumped into the aircraft?

· 157. Read the “Chemistry in Focus” segment Measurement: Past, Present, and Future and answer the following questions.

a. Give three examples of how developing sophisticated measuring devices is useful in our society.

b. Explain how advances in measurement abilities can be a problem.

· 158. The “Chemistry in Focus” segment Measurement: Past, Present, and Future states that hormones can be detected to a level of g/L. Convert this level to units of pounds per gallon.

ChemWork Problems

These multiconcept problems (and additional ones) are found interactively online with the same type of assistance a student would get from an instructor.

· 159.

Complete the following table:

 Number Exponential Notation Number of Significant Figures

· 160.

For each of the mathematical expressions given:

a. Tell the correct number of significant figures for the answer.

b. Evaluate the mathematical expression using correct significant figures in the result.

 Number of Significant Figures Result

· 161.

The longest river in the world is the Nile River with a length of mi. How long is the Nile in cable lengths, meters, and nautical miles?

Use these exact conversions to help solve the problem:

· 162.

Secretariat is known as the horse with the fastest run in the Kentucky Derby. If Secretariat’s record -mi run lasted minute seconds, what was his average speed in m/s?

· 163.

A friend tells you that it is outside. What is this temperature in Celsius?

· 164.

The hottest temperature recorded in the United States is in Greenland Ranch, California. The melting point of phosphorus is . At this temperature, would phosphorus be a liquid or a solid?

· 165.

The density of osmium (the densest metal) is . What is the mass of a block of osmium with dimensions ?

· 166.

The radius of a neon atom is pm, and its mass is g. What is the density of the atom in grams per cubic centimeter ? Assume the atom is a sphere with .

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