Name Block Pre-Lab 0.2 Reading: Measurement section 1 Description and Measurement Before You Read Weight, height, and length are common measurements. List at least five things you can measure. What You ll Learn how to estimate how to round a number the difference between precision and accuracy Read to Learn Measurement A measurement is a way to describe objects and events with numbers. You use measurements to answer questions like how much, how long, or how far. You can measure how much sugar to use in a recipe, how long a snake is, and how far it is from home to school. You also can measure height, weight, time, temperature, volume, and speed. Every measurement has a number and a unit of measure. There are many different units of measure. Some are meter, liter, and gram. Study Coach Make an Outline Make an outline of the main ideas in this section. Use the headings in the section as major headings. Be sure to include all words in bold. How do measurements describe events? Events like races can be described with measurements. In the 2000 summer Olympics, Marion Jones of the United States won the women s 100-m dash in a time of 10.75 s. In this example, measurements tell about the year of the race, its length, and the runner s time. The name of the event, the runner s name, and her country are not measurements. Estimation What happens if you want to know the size of something but it is too large to measure or you don t have a ruler? You can use estimation to make a rough guess about the size of an object. You can use the size of one object you know to help you estimate the size of another object. Estimation can help when you are in a hurry or don t need an exact measurement. You will get better at estimation with practice. 1
Picture This 1. Draw and Compare You can show how the tree is about twice as tall as the person. Draw another person the same height that is standing on the shoulders of the person in the figure. 2. Identify What word tells you that a measurement is an estimate? 3. Apply Give a time when estimating might be helpful. How do you estimate measurements? You can compare objects to estimate a measurement. For example, the tree in the figure is too tall to measure. You can estimate the height of the tree by comparing it to the height of the person. The tree is about twice the height of the person. If the person is about 1.5 m tall, the tree must be 2 1.5 m, or about 3 m tall. Estimated measurements often use the word about. For example, a soccer ball weighs about 400 g. You can walk about 5 km in an hour. When you see or hear the word about with a measurement, the measurement is an estimation. When is estimation used? Estimation is not only used when an exact measurement cannot be made. It is also used to check that an answer is reasonable. A reasonable answer makes sense. Suppose you calculate a friend s running speed as 47 m/s. Does it make sense that your friend can run that fast? Think about how far 47 m is. That s almost a 50-m dash. That means your friend could run a 50-m dash in about 1 s. Can your friend do that? No, he can t. So, 47 m/s is too fast and is not a reasonable answer. You need to check your work. Precision Precision describes how close measurements are to each other. Some measurements are more precise than others. Suppose you measure the distance from home to school four times. Each time you get 2.7 km. Your neighbor measures the same distance four times. He measures 2.9 km two times and 2.7 km two times. Your measurements are closer to each other than your neighbor s measurements. So, your measurements are more precise. The timing for Olympic events has become very precise. Years ago, events were measured to tenths of a second. Now they are measured to hundredths of a second. The instruments we use to measure today are more precise than those used years ago. 2
Accuracy Accuracy is the closeness of a measurement to the true value. Suppose you measured the length of your shoelace two times. One time you measured 12.5 cm and the other time you measured 12.3 cm. Your measurements are precise because they are close together. However, if the shoelace is actually 13.5 cm long, the measurements are not accurate. 4. Apply Give another example of a measurement that is precise but not accurate. What makes a good measurement? A good measurement must be both precise and accurate. A precise measurement is not always a good measurement. A watch that has a second hand is more precise than a watch without one. But, the watch with the second hand could be set 1 hour earlier or later than the real time. In that case, the watch would not be accurate at all. Since the time on the watch is precise but not accurate, the time on the watch is not a good measurement. How do you round a measurement? Suppose you need to measure the length of the sidewalk outside your school. You could measure to the nearest millimeter. But, you probably only need to know the length to the nearest meter or tenth of a meter. Suppose you find that the length of the sidewalk is 135.481 m. How do you round this number to the nearest tenth of a meter? Follow these two steps: 1. Look at the digit to the right of the place being rounded to. If the digit is 0, 1, 2, 3, or 4, the digit being rounded to stays the same. If the digit is 5, 6, 7, 8, or 9, the digit being rounded to increases by one. So, to round to the nearest tenth of a meter, look for the digit in the tenths place, 4. Find the digit to the right of 4. The 4 increases to 5 because the digit to the right of 4 is 8. 2. Look at the digit being rounded to. Then look at the digits to its right. If those digits are to the right of a decimal, they are removed. If they are to the left of a decimal, change them to zeros. For example, 432.9 rounded to the nearest hundred is 400. Since the 9 is to the right of the decimal, it is removed. 5. Rounding Values What is 135.481 m rounded to the nearest ten meters? So, 135.481 rounded to the nearest tenth of a meter is 135.5 m. 3
Some measurements are not precise. If a measurement doesn t need to be precise, you can round your measurement. For example, suppose you want to divide a 2-L bottle of soda equally among seven people. When you use a calculator to divide 2 by 7, you get 0.285 714 28. You can round this number to 0.3. This is a little less than 0.333, or 1 3.You pour a little less than 1 3 L of soda for each person. What are significant digits? Significant digits are the number of digits that show the precision of a number. For example, 18 cm has two significant digits: 1 and 8. There are four significant digits in 19.32 cm: 1, 9, 3, and 2. All non-zero digits are significant digits. Sometimes zeros are significant and sometimes they are not. Use these rules to decide if a zero is a significant digit. 6. Counting Significant Digits How many significant digits are in 28.070? Rule Example Number of Significant Digits Always significant Final zeros after a decimal point 4.5300 5 Zeros between other digits 502.0301 7 Not significant Zeros at the beginning of a number 0.00059 2 May be significant Zeros in whole numbers 16,500 3 or 5 How do you calculate with significant digits? There are rules to follow when deciding the number of significant digits in the answer to a problem. 7. Calculate What is 13.2 4.628, rounded to the nearest significant digit? Show your work. Multiplying or Dividing First, count the significant digits in each number in your problem. Then, multiply or divide. Your answer must have the same number of significant digits as the number with fewer significant digits in the problem. If it does not, you must round your answer. 6.14 5.6 34.384 3 digits 2 digits round to 2 digits Adding or Subtracting When you add or subtract, find the least precise number in the problem (the number with the fewest decimal places). Then add or subtract. Your answer can show only as many decimal places as the least precise number. If it does not, you must round your answer. 6.14 (hundredths) 5.6 (tenths) 11.74 (round to the tenths) 4
After You Read Mini Glossary accuracy: the closeness of a measurement to the actual measurement or value estimation: a method used to guess the size of an object measurement: a way to describe objects and events with numbers precision: describes how close measurements are to each other 1. Review the terms and their definitions in the Mini Glossary. How is precision different from accuracy? 2. Complete the chart that shows how to round a number. Look at digit to the of the place being rounded to. If the digit is less than 5, the digit being rounded to. If the digit is 5 or greater, the digit being rounded to. If digit(s) to the right of the digit being rounded are to the right of a decimal, they are. If they are to the left of a decimal, they are. 3. You were asked to make an outline as you read this section. Did your outline help you learn about measurement? What did you do that seemed most helpful? 5
Pre-Lab 0.2 Reading: Measurement section 2 Standards of Measurement Before You Read If someone asked you how wide your desk is, how would you measure it? Would you measure using inches, centimeters, feet, yards, or meters? Write why you selected this unit of measure. What You ll Learn SI units and symbols for length, volume, mass, density, time, and temperature how to convert related SI units Read to Learn Units and Standards A standard is an exact quantity that people agree to use to compare measurements. A standard is always exactly the same quantity when it is used anywhere in the world. If you and your friend both measure the width of your desk with your hands, will you get the same measure? You can t be sure, because you don t know if your hands are the same size. Study Coach Make an Outline Make an outline of the information in this section. Use headings as each part of the outline. Measurement Systems A measurement is a way to describe the world using numbers. We use measurements to answer questions like how much,how long, or how far. For a measurement to make sense, it must include a number and a unit. Suppose you measure the width of your desk and say its width is 30. We would have to ask Thirty what? Your desk could measure 30 inches in width. Thirty is the number and inches is the unit. In the United States, we commonly use units such as inches, feet, yards, miles, gallons, and pounds. These units are all part of the English system of measurement. Most other nations use the metric system. The metric system is based on multiples of ten. 6
Picture This 1. Recognize Circle the base units that you have seen before. What is the International System of Units? In 1960, an improvement was made to the metric system. This improvement is known as the International System of Units. This system is often abbreviated SI from the French Le Systeme Internationale d Unites. The SI standards are accepted and used by scientists all over the world. Each type of SI measurement has a base unit. The base unit for length is the meter. The names and symbols for the seven base units are in the table below. All other SI units come from these seven base units. SI Base Units Quantity Measured Unit Symbol Length meter m Mass kilogram kg Time second s Electric current ampere A Temperature kelvin K Amount of substance mole mol Intensity of light candela cd Picture This 2. Identify Which of the following is the smallest? (Circle your choice.) a. decigram b. nanogram c. milligram d. kilogram What are SI prefixes? The SI system is easy to use because it is based on multiples of ten. A prefix is added to the name of the base unit to indicate how many multiples of ten it should include. For example, the prefix kilo- means 1,000. That means that one kilometer is equal to 1,000 meters. This also means that one kilogram equals 1,000 grams. The most commonly used prefixes are shown in the table below. Common SI Prefixes Prefix Symbol Multiplying Factor kilo- k 1,000 deci- d 0.1 centi- c 0.01 milli- m 0.001 micro- 0.000 001 nano- n 0.000 000 001 7
How do you convert between SI units? Sometimes quantities are measured using different units. A teacher has 1.3 L of water for a class experiment. She needs 125 ml to conduct the experiment. To determine if she has enough water, she must first find out how many milliliters of water she has. Conversion Factors A conversion factor is used to change measurements from one unit to another. A conversion factor is a ratio that equals one. For a ratio to equal one, the numerator and denominator must have the same value. The numerator of a conversion factor should be the new unit. The denominator should be the old unit. For example, if you are converting liters to milliliters, use the following conversion factor. n ew old unit unit 100 0 ml 1 L To find out how much water she has in centiliters, the teacher multiplies the amount of water she has by the conversion factor. 1.3 L 100 0 ml 1 L 1.3 L 100 0 ml 1 L 1.3 1000 ml 1,300 ml The teacher has 1,300 ml of water. That is enough for her experiment! Measuring Distance In science, the word length is used to describe the distance between two points. The SI base unit of length is the meter, m. A baseball bat is about a meter long. Metric rulers and metersticks are commonly used to measure length. A meterstick is a little bit longer than a yardstick. 3. Convert Units A length of rope measures 3,000 millimeters. How long is it in meters? 3,000 mm 1,00 1 3,0 00 1 m 1 1,000 3, 000 m 1, 000 m 0 mm 4. Convert Units A small lizard weighs about 14,000 grams. How many kilograms does it weigh? 8
How do you choose a unit of length? When measuring distance, it is important to choose the proper unit. The unit you choose will depend on the object being measured. For example, you would measure the length of a pencil in centimeters. The length of your classroom would be measured in meters. The distance from school to your house would be measured in kilometers. By choosing the best unit, you can avoid very large or very small numbers. It is easier to say something is 21 km rather than saying it is 21,000 m. 5. Define In the calculations for finding the volume of the van, ( m m m) is rewritten as m 3. The 3 in m 3 is called an exponent. What does an exponent represent? Measuring Volume Volume is the amount of space an object fills. The volume of a rectangular solid, such as a brick, is found by multiplying its length, width, and height (V l w h). If the sides of the brick were measured in centimeters, cm, the volume would be expressed in cubic centimeters, cm 3.When you multiply all three measurements, you multiply cm three times, once with each measurement. The result is cm 3.Ifyou were trying to find out how much space there is in a moving van, you would measure the van using meters. Its volume would be expressed in cubic meters, m 3.Let s find the volume of this van. 2 m 4 m 3 m 6. Calculate What is the volume of a brick that has a length of 20 cm, a width of 6 cm, and a height of 5 cm? Show your work. First find the length, width, and height of the van. Length 4 m Width 2 m Height 3 m Substitute these values into the formula for finding volume. V l w h 4 m 2 m 3 m (4 2 3)(m m m) 24 m 3 The volume of the moving van is 24 m 3. 9
How do you measure the volume of a liquid? Measuring the volume of a liquid in a container is different than measuring a solid object because the liquid does not have sides. To find the volume of a liquid, you first must know how much liquid the container can hold. This is called the capacity of the container. The most common units for expressing the volume of liquids are liters, L, and milliliters, ml. A milliliter is equal in volume to 1 cm 3.So, the volume of 1 L equals 1,000 cm 3.Look at food cans and bottles to see how these measurements are used. Measuring Matter Mass is the measure of how much matter is in an object. A golf ball and a table tennis ball are about the same size. If you pick up both, you notice a difference. The golf ball has more matter, or mass, than the table tennis ball. What is density? Another property of matter is density. The density of an object is the amount of mass in one cubic unit of volume of the object. You can find density by dividing an object s mass by its volume. The formula for density is: D m V In the formula, D represents density, m represents an object s mass, and V represents the object s volume. Suppose an object weighs 10 g and has a volume of 2 cm 3. Find the density of the object. 10 g 2 3 5 g/cm cm 3 If two objects are the same size and one object has a greater mass, it also has a greater density. This is because there is more mass in one cubic unit of volume. The golf ball and the table tennis ball have about the same volume. However, the golf ball has a greater mass. This means that the golf ball also has a greater density. 7. Measure in SI What are the most common units for expressing the volume of liquids? 8. Calculate Suppose an object weighs 15 g and has a volume of 5 cm 3. What is the density of the object? 9. Compare Which has a greater density, a bowling ball or a volleyball? Measuring Time Sometimes scientists need to keep track of how long it takes something to happen. The unit of time in the SI system is second, s. Seconds are usually measured with a clock or a stopwatch. 10
10. Describe What do you add to a temperature in Celsius to convert it to a temperature in kelvin? Measuring Temperature Sometimes scientists need to measure how much something heats up or cools down. Temperature is a measure of how hot or cold something is. Later, you will learn the scientific meaning of temperature. What is Fahrenheit? The temperature measurement you are probably most familiar with is the Fahrenheit (F) scale. The Fahrenheit scale is based on the temperature of the human body, 98.6. On this scale, water freezes at 32 F and boils at 212 F. What is Celsius? Scientists use the Celsius (C) scale to measure temperature. On this scale, water freezes at 0 C and boils at 100 C. The scale is divided into 100 equal divisions, or degrees, between the freezing point and the boiling point of water. What is Kelvin? The SI unit for measuring temperature is kelvin (K). On the Kelvin scale, 0 K is called absolute zero. This is the coldest possible temperature. Absolute zero is equal to 273 C, which is 273 below the freezing point of water. The divisions on the Kelvin and Celsius scales are the same size. This makes it easy to convert between the two scales. Water freezes at 0 C. To convert to Kelvin, you add 273 to the Celsius temperature. So, on the Kelvin scale, water freezes at 273 K. Water boils at 100 C. So, on the Kelvin scale, water boils at 373 K. Picture This 11. Label each thermometer in the diagram with its correct temperature scale. 11
After You Read Mini Glossary density: the mass per unit volume of a material mass: the measurement of the quantity of matter in an object SI: the International System of Units standard: an exact quantity that people agree to use to compare measurements volume: the amount of space occupied by an object 1. Review the terms and their definitions in the Mini Glossary. Write, in your own words, a sentence that explains how mass affects an object s density. 2. Complete the chart below to organize the information from this section. For each unit include the unit s name, what it measures, and its symbol. 3. Think about what you have learned. Write a way to help you remember the meaning of volume. 12