1. Accuracy and Precision
9-1
Accuracy and Precision
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. Accuracy and Precision
Course 2
9-1
Accuracy and Precision
Warm Up
Convert.
hr = ____ days
kg = ____ g
qt = ____ pt
mm = ____ cm 9
3700 9
0.72

3. Accuracy and Precision
Course 2
9-1
Accuracy and Precision
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 that 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.

4. Accuracy and Precision
Course 2
9-1
Accuracy and Precision
Learn to compare the precision of measurements and to determine acceptable levels of accuracy.

5. Insert Lesson Title Here
Course 2
9-1
Accuracy and Precision
Insert Lesson Title Here
Vocabulary
precision
accuracy
significant digits

6. Accuracy and Precision
Course 2
9-1
Accuracy and Precision
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 modern scientists conducted the measurement with greater precision. Precision is the level of detail an instrument can measure.

7. Accuracy and Precision
Course 2
9-1
Accuracy and Precision
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.

8. Additional Example 1: Judging Precision of Measurements
Course 2
9-1
Accuracy and Precision
Additional Example 1: Judging Precision 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.

9. Insert Lesson Title Here
Course 2
9-1
Accuracy and Precision
Insert Lesson Title Here
Check It Out: Example 1
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.

10. Accuracy and Precision
Course 2
9-1
Accuracy and Precision
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 non-significant.

11. Number of Significant Digits
Course 2
9-1
Accuracy and Precision
The table shows the rules for identifying significant digits.
Rule
Example
Number of 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

12. Additional Example 2: Identifying Significant Digits
Course 2
9-1
Accuracy and Precision
Additional Example 2: Identifying Significant Digits
Determine the number of significant digits in each measurement.
A km
The digits 3, 4, and 7 are nonzero digits, and 0
is between two nonzero digits.
So has 4 significant digits.
B L
The digits 7 and 6 are nonzero digits, and 0 is to the right of the decimal after the last nonzero digit.
So L has 3 significant digits.

13. Insert Lesson Title Here
Course 2
9-1
Accuracy and Precision
Insert Lesson Title Here
Check It Out: Example 2
Determine the number of significant digits in each measurement.
A mi
The digits 2, 3, and 4 are nonzero digits, and 0 is between two nonzero digits.
So mi has 4 significant digits.
B 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 kg has 3 significant digits.

14. Accuracy and Precision
Course 2
9-1
Accuracy and Precision
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.

15. Accuracy and Precision
Course 2
9-1
Accuracy and Precision
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.

16. Insert Lesson Title Here
Course 2
9-1
Accuracy and Precision
Insert Lesson Title Here
Check It Out: Example 3
Calculate 15 ft – 3.8 ft. Use the correct number of significant digits in the answer. 15
– 3.8
0 digits to the right of the decimal point.
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.

17. Accuracy and Precision
Course 2
9-1
Accuracy and Precision
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.

18. Accuracy and Precision
Course 2
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Accuracy and Precision
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 mm
Round the product so that it has 2 significant digits.

19. Insert Lesson Title Here
Course 2
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Accuracy and Precision
Insert Lesson Title Here
Check It Out: Example 4
Calculate 2.43 m · 31 m. Use the correct number of digits in the answer.
2.43
3 significant digits.
 31
2 significant digits.
75.33
75 m 
Round the product so that it has two
significant digits.

20. Accuracy and Precision Insert Lesson Title Here
Course 2
9-1
Accuracy and Precision
Insert Lesson Title Here
Lesson Quiz: Part I
1. Which measurement is more precise,
10 in. or 1 ft?
Determine the number of significant digits in each measurement.
Calculate. Use the correct number of significant digits.
4. 72 – · 4.1
10 in. 4 2 71 75

21. Accuracy and Precision Insert Lesson Title Here
Course 2
9-1
Accuracy and Precision
Insert Lesson Title Here
Lesson Quiz: Part II
6. A veterinarian’s 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