Transcript Chapter 2 Section 1 Notes and packet

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.
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ch 2, sect 1 Study Guide
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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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Description and Measurement
1
Measurement
• 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.
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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Description and Measurement
1
Measurement
• 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.”
Description and Measurement
1
Describing Events
• Measurement also can describe events.
• In the 1956 summer Olympics, sprinter Betty
Cuthbert of
Australia came
in first in the
women’s 200-m
dash.
Description and Measurement
1
Describing Events
• She ran the race in 23.4 s.
• Measurements convey information about the
year of the race,
its length, the
finishing order,
and the time.
Description and Measurement
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Estimation
• Estimation can help you make a rough
measurement of an object.
• 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.
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2. Estimation can check that an answer is
_reasonable__.
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3. When you estimate, you often use the word
_about_.
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Description and Measurement
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Estimation
• In many instances, estimation is used on
a daily basis.
• For example, a caterer prepares for each
night’s crowd based on an estimation of
how many will order each entrée.
Description and Measurement
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Using Estimation
• You can use comparisons to estimate
measurements.
• 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.
Description and Measurement
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Using Estimation
• Estimation also is used to check that an
answer is reasonable. Suppose you calculate
your friend’s running speed as 47 m/s.
• 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.
Description and Measurement
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Precision and Accuracy
• Precision is a description of how close
measurements are to each other.
• 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
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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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Description and Measurement
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Precision and Accuracy
• 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.
Description and Measurement
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Precision and Accuracy
• The term precision also is used when
discussing the number of decimal places
a measuring device can measure.
• A clock with a
second hand is
considered
more precise
than one with
only an hour
hand.
Description and Measurement
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Degrees of Precision
• The timing for events has become more
precise over the years.
• Events that were measured in tenths of a
second 100 years ago are measured to the
hundredth of a second today.
Description and Measurement
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Accuracy
• When you compare a measurement to the
real, actual, or accepted value, you are
describing accuracy.
• A watch with a second hand is more precise
than one with only an hour hand, but if it is
not properly set, the
readings could be off
by an hour or more.
Therefore, the watch
is not accurate.
Description and Measurement
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Rounding a Measurement
• Suppose you need to measure the length of
the sidewalk outside your school.
• 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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Description and Measurement
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Rounding a Measurement
• To round a given value, follow these steps:
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.
Description and Measurement
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Rounding a Measurement
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.
Description and Measurement
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Precision and Number of Digits
• 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 Digits
Example
Number of
Significant
Figures
Scientific
Notation
0.00682
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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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Description and Measurement
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Using Precision and
Significant Digits
• 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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Description and Measurement
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Using Precision and
Significant Digits
• 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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Description and Measurement
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Following the Rules
• 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.
Description and Measurement
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Following the Rules
• 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.
Section Check
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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
_______.
Section Check
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Answer
The answer is
measurement. Measurement
is used to answer questions
such as: How long? How
many? How far?
Section Check
1
Question 2
It 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. assignation
B. estimation
C. pagination
D. salination
Section Check
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Answer
The answer is B. You can
use estimation to get a
rough measurement of an
object.
Section Check
1
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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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.
accurate
(the average is
accurate)
not precise
precise
not accurate
accurate
and
precise
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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 Digits
Example
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.
300.0
3
4
3.00 x 102
3.000 x 102
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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