chapter 2 section 1 notes and packet goal goal: as a result of this lesson, you will be able to...

Chapter 2 Section 1

Notes and packet

Goal• Goal: As a result of this lesson, you will be

able to understand how reasonable an estimate is by estimating, rounding numbers, distinguish between precision and accuracy in measurement.

Packet page 3 ch 2, sect 1 Study Guide

• A. _Measurement_—describes the world using numbers• *Measurement is a way to describe the world with numbers. • 1. Types of measurement—distance, time, speed, volume, mass• • 2. Measurement can also help describe __events________.• • B. Approximated measurement based on previous experience is __estimation__.• *Estimation can help you make a rough measurement of an object by guessing.

• 1. Estimation is useful when actual measurements are __not easily_ • made.• • 2. Estimation can check that an answer is _reasonable__.• • 3. When you estimate, you often use the word _about_.

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• C. Precision and accuracy• • 1. _Precision_—a description of how close measurements are to each other• * If four measurements of a flag pole indicate that it is 45.21 m high each time, these • measurements have a high degree of precision.• * Precision describes how closely individual measurements agree with each other.

• a. Used to discuss number of _decimal places a measuring device can measure• • b. Degrees of Precision—today’s measuring devices are more _precise_.• • 2. _Accuracy_—comparison of measurement to its real, or actual, value• • 3. Precision and accuracy are important in many _medical_ procedures.• • 4. Measurements can be _rounded_ when precision is not needed.• * 11.85 seconds rounded to the nearest second is 12 seconds.• • 5. __Significant digits__—reflect true precision of a calculation• * The number of digits that reflect the precision of a calculation are called significant digits or • significant figures.

• a. Multiplication or division—measurement with the _fewest_ digits determines the number of • significant digits.• • b. Addition or subtraction—significance determined to the place value of the __ least__ precise• measurement

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• Measurement is a way to describe the world with numbers.

• It answers questions such as how much, how long, or how far.

• Measurement can describe the amount of milk in a carton, the cost of a new compact disc, or the distance between your home and your school.

Measurement

Description and MeasurementDescription and Measurement

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Notes

• A. _Measurement_—describes the world using numbers

• 1. Types of measurements—distance, time,

speed, volume, mass • 2. Measurement can also help describe

__events________.

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• In scientific endeavors, it is important that scientists rely on measurements instead of the opinions of individuals.

• You would not know how safe the automobile is if this researcher turned in a report that said, “Vehicle did fairly well in head-on collision when traveling at a moderate speed.”

Measurement


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• Measurement also can describe events.

Describing Events


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• In the 1956 summer Olympics, sprinter BettyCuthbert of Australia came in first in the women’s 200-m dash.

Describing Events


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• She ran the race in 23.4 s.

• Measurements convey information about theyear of the race, its length, the finishing order, and the time.

• Estimation can help you make a rough measurement of an object.

Estimation


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• Estimation is a skill based on previous experience and is useful when you are in a hurry and exact numbers are not required.

Notes• B. Approximated measurement based on

previous experience is __estimation__.• *Estimation can help you make a rough

measurement of an object by guessing.• 1. Estimation is useful when actual measurements are

__not easily_ made. • 2. Estimation can check that an answer is

_reasonable__. • 3. When you estimate, you often use the word

_about_.

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• In many instances, estimation is used on a daily basis.

Estimation


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• For example, a caterer prepares for each night’s crowd based on an estimation of how many will order each entrée.

• You can use comparisons to estimate measurements.

Using Estimation


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• When you estimate, you often use the word about.

• For example, doorknobs are about 1 m above the floor, a sack of flour has a mass of about 2 kg, and you can walk about 5 km in an hour.

• Estimation also is used to check that an answer is reasonable. Suppose you calculate your friend’s running speed as 47 m/s.

Using Estimation


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• Can your friend really run a 50-m dash in 1 s? Estimation tells you that 47 m/s is unrealistically fast and you need to check your work.

• Precision is a description of how close measurements are to each other.

Precision and Accuracy


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• Suppose you measure the distance between your home and your school five times and determine the distance to be 2.7 km.

Notes• C. Precision and accuracy • ..\ch 2 videos\Accuracy and Precision.mp4

good• 1. _Precision_—a description of how close

measurements are to each other• * If four measurements of a flag pole indicate

that it is 45.21 m high each time, these measurements have a high degree of precision.

• * Precision describes how closely individual measurements agree with each other.

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Notes• a. Used to discuss number of _decimal

places a measuring device can measure• b. Degrees of Precision—today’s measuring

devices are more precise. • 2. _Accuracy_—comparison of measurement

to its real, or actual, value• 3. Precision and accuracy are important in

many _medical_ procedures.

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• Suppose a friend measured 2.7 km on two days, 2.8 km on two days, and 2.6 km on the fifth day.

• Because your measurements were closer to each other than your friend’s measurements, yours were more precise.

• The term precision also is used when discussing the number of decimal places a measuring device can measure.



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• A clock with a second hand is considered more precise than one with only an hour hand.

• The timing for events has become more precise over the years.

Degrees of Precision


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• Events that were measured in tenths of a second 100 years ago are measured to the hundredth of a second today.

• When you compare a measurement to the real, actual, or accepted value, you are describing accuracy.

Accuracy


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• A watch with a second hand is more precise than one with only an hour hand, but if it isnot properly set, the readings could be off by an hour or more. Therefore, the watch is not accurate.

• Suppose you need to measure the length of the sidewalk outside your school.

Rounding a Measurement


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• If you found that the length was 135.841 m, you could round off that number to the nearest tenth of meter and still be considered accurate.

Notes

• 4. Measurements can be _rounded_ when precision is not needed.

• * 11.85 seconds rounded to the nearest second is 12 seconds.

• ..\ch 2 videos\Rounding Numbers.mp4 weak!

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• To round a given value, follow these steps:



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1. Look at the digit to the right of the place being rounded to.

• If the digit to the right is 0, 1, 2, 3, or 4, the digit being rounded to remains the same.

• If the digit to the right is 5, 6, 7, 8, or 9, the digit being rounded to increases by one.



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2. The digits to the right of the digit being rounded to are deleted if they are also to the right of a decimal. If they are to the left of a decimal, they are changed to zeros.

Precision and Number of Digits


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• Suppose you want to divide a 2-L bottle of soft drink equally among seven people.

• Will you measure exactly 0.285 714 285 L for each person?

• No. All you need to know is that each person gets about 0.3 L of soft drink.

Significant digits

• Where do you place the decimal when doing scientific notation?

• 345= 3.45• 0.375= 3.75• 0.0000054= 5.4

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Significant DigitsExample Number of

Significant Figures

Scientific Notation

0.00682 3 6.82 x 10-3 Leading zeros are not

significant.

1.072 4 1.072 (x 100)

Imbedded zeros are always significant.

300 1 3 x 102 Trailing zeros are significant only if

the decimal point is

specified.

300. 3 3.00 x 102

300.0 4 3.000 x 10236

Using Precision and Significant Digits


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• The number of digits that truly reflect the precision of a number are called the significant digits or significant figures. • Digits other than zero are always significant. • Final zeros after a decimal point (6.545 600 g)

are significant.• Zeros between any other digits (507.0301 g) are

significant. • Initial zeros (0.000 2030 g) are NOT significant.

Notes

• 5. __Significant digits__—reflect true precision of a calculation

• * The number of digits that reflect the precision of a calculation are called significant digits or significant figures.

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Using Precision and Significant Digits


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• Zeros in a whole number (1650) may or may not be significant.

• A number obtained by counting instead of measuring, such as the number of people in a room or the number of meters in a kilometer, has infinite significant figures.

Notes• a. Multiplication or division—

measurement with the _fewest_ digits determines the number of significant digits.

• b. Addition or subtraction—significance determined to the place value of the __least__ precise measurement.

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Following the Rules


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• For multiplication and division, you determine the number of significant digits in each number in your problem. The significant digits of your answer are determined by the number with fewer digits.

Following the Rules


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• For addition and subtraction, you determine the place value of each number in your problem. The significant digits of the answer are determined by the number that is least precise.

11Section CheckSection Check

Question 1

How many oranges can fit inside a given crate? How much rain fell on your town during the last thunderstorm? These are questions of _______.


Answer

The answer is measurement. Measurement is used to answer questions such as: How long? How many? How far?


Question 2It isn’t always necessary to know exactly how much or exactly how fast. As a rough way of looking at your data, you can use _______.

A. assignationB. estimationC. paginationD. salination


Answer

The answer is B. You can use estimation to get a rough measurement of an object.


Question 3

Round 1.77 g to the nearest tenth of a gram.

Answer

The answer is 1.8 grams. The digit in the hundreds column is above 5, so you round up the digit in the tens column.

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accurate(the average is

accurate)not precise

precisenot accurate

accurateand

precise

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PRECISION VERSUS ACCURACY Accuracy- refers to how closely a measured value agrees with the correct value.Precision -refers to how closely individual measurements agree with each other.

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Significant digits

• Where do you place the decimal when doing scientific notation?

• 345= 3.45• 0.375= 3.75• 0.0000054= 5.4

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Significant DigitsExample Number of

Significant Figures

Scientific Notation

0.00682 3 6.82 x 10-3 Leading zeros are not significant.

1.072 4 1.072 (x 100)

Imbedded zeros are always significant.

300 1 3 x 102 Trailing zeros are significant only if the decimal point

is specified.

300. 3 3.00 x 102

300.0 4 3.000 x 102

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7 • Section 1 (page 23)• 1. Sample questions:• a. How high can it jump?• b. How long is its tail?• c. How much does it weigh?• d. How much does it eat?• 2. Sample questions:• a. How tall is it?• b. What is the inside temperature?• c. How fast is lava flowing out?• d. How often does it erupt?• 3. about 3 cm• 4. about 1/2 meter• 5. about 1 mm• 6. Answers will vary.

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• 7. Student B’s is more accurate because it is closer to the true value.

• 8. It is precise to the nearest hundredth of a centimeter.

• 9. 10 cm• 10. 9.8 cm

chapter 2 section 1 notes and packet goal goal: as a result of this lesson, you will be able to...

Documents

measurement description

packet slide

precise measurement

approximated measurement

rough measurement

comparison of measurement

true precision

events description