9-1 Accuracy and Precision

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpConvert.

1. 216 hr = ____ days

2. 3.7 kg = ____ g

3. 4.5 qt = ____ pt

4. 7.2 mm = ____ cm

3700

9

Course 2

9-1 Accuracy and Precision

9

0.72

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.

Course 2

9-1 Accuracy and Precision

Learn to compare the precision of measurements and to determine acceptable levels of accuracy.

Course 2

9-1 Accuracy and Precision

Vocabulary

precisionaccuracysignificant digits

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Course 2

9-1 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.

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.

Choose the more precise measurement in each pair.

Additional Example 1: Judging Precision of Measurements

Course 2

9-1 Accuracy and Precision

A. 13 oz, 1 lb

Since an ounce is a smaller unit than apound, 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.

Check It Out: Example 1

Choose the more precise measurement in each pair.

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Course 2

9-1 Accuracy and Precision

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.

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.

Course 2

9-1 Accuracy and Precision

Rule ExampleNumber of

Significant Digits

• Nonzero digits

• Zeros between significant digits

• Zeros after the last nonzero digit and to the right of a decimal point

45.7

78,002

0.0040

3 significant digits

5 significant digits

2 significant digits

The table shows the rules for identifying significant digits.

Determine the number of significant digits in each measurement.

Additional Example 2: Identifying Significant Digits

Course 2

9-1 Accuracy and Precision

A. 304.7 km

The digits 3, 4, and 7 are nonzero digits, and 0is between two nonzero digits.

B. 0.0760 L

The digits 7 and 6 are nonzero digits, and 0 is to the right of the decimal after the last nonzero digit.

So 304.7 has 4 significant digits.

So 0.0760 L has 3 significant digits.

Check It Out: Example 2

Determine the number of significant digits in each measurement.

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Course 2

9-1 Accuracy and Precision

A. 230.4 mi

The digits 2, 3, and 4 are nonzero digits, and 0 is between two nonzero digits.

B. 0.0460 kgThe digits 4 and 6 are nonzero digits, and the 0 is to the right of the decimal after the last nonzero digit.

So 230.4 mi has 4 significant digits.

So 0.0460 kg has 3 significant digits.

Course 2

9-1 Accuracy and Precision

When you are adding and subtractingmeasurements, the answer shouldhave the same number of digits tothe right of the decimal point as themeasurement with the least number of digits to the right of the decimal point.

Calculate 67 ft – 0.8 ft. Use the correct number of significant digits in the answer.

Additional Example 3: Using Significant Digits in Addition or Subtraction

Course 2

9-1 Accuracy and Precision

67 – 0.8

66.2 66 ft1 digit to the right of the decimal pointRound the difference so it has no digits to the right of the decimal point.

0 digits to the right of the decimal point

Check It Out: Example 3

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Course 2

9-1 Accuracy and Precision

Calculate 15 ft – 3.8 ft. Use the correct number of significant digits in the answer.

15 – 3.8

11.2 11 ft

1 digit to the right of the decimal point.

Round the difference so it has no digits to the right of the decimal point.

0 digits to the right of the decimal point.

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.

Calculate 19.8 mm · 1.4 mm. Use the correct number of significant digits in the answer.

Additional Example 4: Using Significant Digits in Multiplication or Division

Course 2

9-1 Accuracy and Precision

19.8 1.427.72

3 significant digits.2 significant digits

Round the product so that it has 2 significant digits.

28 mm

Check It Out: Example 4

Calculate 2.43 m · 31 m. Use the correct number of digits in the answer.

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Course 2

9-1 Accuracy and Precision

2.43 31

75.33

3 significant digits.

2 significant digits.

Round the product so that it has two significant digits.

75 m

Lesson Quiz: Part I

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. Use the correct number of significant digits.

4. 72 – 0.8 5. 18.3 · 4.1

4

10 in.

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2

71

Course 2

9-1 Accuracy and Precision

75

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

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Course 2

9-1 Accuracy and Precision