Chapter 2 Review Math 1030Section A.1: You Can’t Add Apples and OrangesDefinition of unitsThe units of a quantity describe what is measured or counted.We cannot add or subtract numbers with different units, but we can multiply a nd divide quantities withdifferent units.There are four different operations that we are allowed to do with different units:(1) division(2) raising to second power(3) raising to third power(4) multiplicationIdentifying units in a problemIn order to understand what a problem is about, the first thing to do is to look at the units involved inthe problem.Ex.1Identify the units in the price for gasoline found by dividing its total cost in euros by the number of litersof gas.Ex.2Identify the units in the volume found by multiplying an area measured in square meters by a dep thmeasured in centimeters.Section A.2: Unit ConversionsUnit conversionsIt is very important to understand how we can convert one unit to another one.Ex.3Convert 5 meters into kilometers.1Chapter 2 Review Math 1030Ex.4How many seconds are there in one year?Ex.5Convert 1 gram2to hectogram2.Ex.6You want to carpet a room that measures 10 by 12 feet, ma king an area of 120 square feet. But c arpet isusually sold by the square yard rather than by the square f oot. How many square yards of carpet do youneed?2Chapter 2 Review Math 1030Ex.7You are preparing a vegetable garden that is 20 meters long and 12 meters wide, and you need enoughsoil to fill it to a depth of 1 meter. The landscape supply store sells soil by the c ubic feet. How much soilshould you order?Ex.8At an italian pizzeria, the price for a pizza is 15 euros. What is the p rice in U.S. dollars? (1 euro =$1.272).Section A.3: Problem Solving with UnitsWorking with units(1) Identify the units involved in the problem. Use the units to help you decide how to approach theproblem and what units to expect in the answer.(2) Perform any operations (addition, multiplication,...) on both the numbers and the associated units.Remember:• You cannot add or subtract numbers with different units (you cannot add apples and oranges),but you can combine different units through multiplication, division or raising to powers.• To make your work with units easier, replace division with multiplication by the reciprocal.(3) When you complete your calcula tions, make sure that your answer has the units you expected. If itdoesn’t, then there is a mistake.3Chapter 2 Review Math 1030Ex.9 Gas Mileage.After a long day of driving, your destination is only 150 miles away. You know that your car gets 30miles per gallon. How much gas do you need in your tank if you want to reach the destination withoutstopping? If you have a 20-gallon tank and the fuel gauge shows it is one-quarter full, will you makeit?4Chapter 2 Review Math 1030Section B.1: Standardized Unit Systems: U.S. an d MetricDifferent system of standardized unitsThere are different systems of standardized units: the international metric system, called SI (from the FrenchSyst`eme International d’Unit´es) and the English system, called the U.S. customary system (USCS).The U.S. Customary System• To measure the lengths of objects we have: inches, feet, yards, miles and others.• To measure weights of objects we have three different ways: Avoirdupois measures, Troy measuresand Apothecary measures. The Avoirdupois measures are commonly used today.• To measure volumes we have two kinds of measures: Liquid measures and Dry measures. Theliquid measures are used in the case of liquid objects as water, beer and so on. The Dry measuresare used in the case of solid objects such as flour.Notice that 1 dry pint = 33.60 in3> 1 liquid pint = 28.88 in3.The International Metric SystemThe basic units of length, mass, time and volume in the metric system are• the meter for length (m);• the kilogram for mass (kg);• the second for time (s);• the liter for volume (L).In the international metric system we use powers of 10 to find all the other units ad we write the new unitsadding a prefix which indicates multiplication by a power of 10.Ex.10At a gas station in Mexico, the price of gasoline is 0.05 p esos per centiliter. What is the price in dollars pergallons?We know that 1 p eso = $0.09136.5Chapter 2 Review Math 1030Ex.11How many square meters are in a square mile?Temperatu re Units: Fahrenheit, Celsius and Kelvi nTemperature UnitsThere are three temperature scales commonly used today: Fahrenheit, Celsius and Kelvin.• The Fahrenheit scale is used in the United States and it is defined so that water freezes at 32◦F andboils at 212◦F .• Internationally, temperature is measured on the Celsius scale, which places the freez ing point ofwater at 0◦C and the boiling point at 100◦C.• The Kelvin scale is used in science and is the same as the Celsius scale except for its zero point: atemperature of 0 K is the coldest possible temperature, known as absolute zero and it correspondto −273.15◦C or −459.67◦F .The conversions are:• from Celsius to Fahrenheit:F = 1.8 C + 32• from Fahrenheit to Celsius:C =F − 321.8• from Celsius to Kelvin:K = C + 273.15• from Kelvin to Celsius:C = K − 273.15.6Chapter 2 Review Math 1030Ex.12Convert 15◦F into Celsius.Ex.13Convert 4 K into Fahrenheit.Section B.2: Units of Energy and PowerDefinition of energyEnergy is what makes matter move or heat up. The international metric unit of energy is the joule.CaloriesFor example, we need energy from food to walk or run. The most familiar energy unit is the food Calorieused to measure the energy our body can draw from food:1 Calorie = 4184 joules.Definition of powerPower is the rate at which energy is used. The international metric unit of energy is the watt:1 watt = 1joules.7Chapter 2 Review Math 1030Ex.14You burn 1200 Calories playing volleyball for 2 hours. What is the average power during the game inwatts? Are you generating enough power to kee p a 100-watt bulb shining? Explain.Definition of kilowatt-hourA kilowatt-hour is a unit of energy:1 kilowatt-hour =1000 joule1 s× 1 hr =1000 joule1 s× 3, 600 s = 3, 600, 000 joule.Ex.15Your electric bill states that you used 2000 kilowatt-hours of energy in November. Determine your totalelectrical energy use, in joules and your average p ower use, in watts.8Chapter 2 Review Math 1030Section B.3: Units of Density and ConcentrationDefinition of densityDensity describes compactness or crowding. There are three d ifferent kinds of d ensities:• Material density is given in