Warm Up

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Warm Up
Problem of the Day
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Lesson Presentation
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Warm Up Convert. 1. 216 hr ____ days 2. 3.7
kg ____ g 3. 4.5 qt ____ pt 4. 7.2 mm ____
cm
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3700
9
0.72
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Problem of the Day Polly found that an empty
bird cage weighs 18 oz. With a bird in it, the
cage weighs 24 oz. Polly calculated the bird must
weigh 6 oz. How far off might that calculation
be?
1 oz in either direction each weight might be
off 0.5 oz in either direction.
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Learn to compare the precision of measurements
and to determine acceptable levels of accuracy.
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Insert Lesson Title Here
Vocabulary
precision accuracy significant digits
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Ancient Greeks used measurements taken
during lunar eclipses to determine that the Moon
was 240,000 miles from the Earth. In 1969, the
distance was measured as 221,463 miles.
There is a difference between these
measurements because the modern scientists
conducted the measurement with greater
precision. Precision is the level of detail an
instrument can measure.
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The smaller the unit an instrument can measure,
the more precise its measurements will be. For
example, a millimeter ruler has greater precision
than a centimeter ruler because it can measure
smaller units.
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Additional Example 1A 1B Judging Precisions of
Measurements
Choose the more precise measurement in each pair.
A. 13 oz, 1 lb
Since an ounce is a smaller unit than a pound, 13
oz is more precise.
B. 52 cm, 52.3 cm
Since 52.3 has the smaller decimal place, 52.3 cm
is more precise.
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Insert Lesson Title Here
Try This Example 1A 1B
Choose the more precise measurement in each pair.
A. 1 gal, 5 qt
Since a quart is a smaller unit than a gallon, 5
quarts is more precise.
B. 5.4 mi, 15,000 m
Since a meter is a smaller unit than a
mile, 15,000 meters is more precise.
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In the real world, no measurement is exact. The
relative exactness of a measurement is its
accuracy. In a measured value, all the digits
that are known to be exact are called significant
digits. Zeros at the end of a whole number are
assumed to be nonsignificant.
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The table shows the rules for identifying
significant digits.
3 significant digits
Nonzero digits
45.7
Zeros between significant digits
5 significant digits
78,002
Zeros after the last nonzero digit and to the
right of a decimal point
2 significant digits
0.0040
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Additional Example 2A 2B Identifying
Significant Digits
Determine the number of significant digits in
each measurement.
A. 304.7 km
The digits 3, 4, and 7 are nonzero digits, and
0 is between two nonzero digits. So 304.7 has 4
significant digits.
B. 0.0760 L
The 7 and 6 are nonzero digits, and 0 is to the
right of the decimal after the last nonzero
digit. So 0.0760 L has 3 significant digits.
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Insert Lesson Title Here
Try This Example 2A 2B
Determine the number of significant digits in
each measurement.
A. 230.4 mi
The digits 2, 3, and 4 are nonzero digits, and 0
is between two nonzero digits. So 230.4 mi has 4
significant digits.
B. 0.0460 kg
The digits 4 and 6 are nonzero digits, and the 0
is to the right of the decimal after the last
nonzero digit. So 0.0460 kg has 3 significant
digits.
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When you are adding and subtracting measurements,
the answer should have the same number of digits
to the right of the decimal point as
the measurement with the least number of digits
to the right of the decimal point.
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Additional Example 3 Using Significant Digits in
Addition or Subtraction
Calculate 67 ft 0.8 ft. Use the correct number
of significant digits in the answer.
67 0.8
0 digits to the right of the decimal point
1 digit to the right of the decimal point
66.2 ? 66 ft
Round the difference so it has no digits to the
right of the decimal point.
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Insert Lesson Title Here
Try This Example 3
Calculate 15 ft 3.8 ft. Use the correct number
of significant digits in the answer.
0 digits to the right of the decimal point.
15 3.8
1 digit to the right of the decimal point.
11.2 ? 11 ft
Round the difference so it has no digits to the
right of the decimal point.
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When you are multiplying and dividing
measurements, the answer must have the same
number of significant digits as the measurement
with the least number of significant digits.
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Additional Example 4 Using Significant Digits in
Multiplication or Division
Calculate 19.8 mm 1.4 mm. Use the correct
number of significant digits in the answer.
19.8
3 significant digits.
? 1.4
2 significant digits
27.72
28
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Round the product so that it has 2 significant
digits.
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Insert Lesson Title Here
Try This Example 4
Calculate 2.43 31. Use the correct number of
digits in the answer.
2.43
3 significant digits.
? 31
2 significant digits.
75.33
75
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Round the product so that it has two significant
digits.
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Insert Lesson Title Here
Lesson Quiz Part 1
1.Which measurement is more precise, 10 in. or
1 ft? Determine the number of significant
digits in each measurement. 2. 6.004 3.
0.070 Calculate. Give the answer with the correct
number of significant digits. 4. 72 0.8 5. 18.3
4.1
10 in.
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2
71
75
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Insert Lesson Title Here
Lesson Quiz Part 2
6. A veterinarians assistant finds that a dog
weighs 11 kg. What is the least and the most the
dog might really weigh?
10.5 kg to 11.5 kg