Using and Expressing Measurements

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# Using and Expressing Measurements - PowerPoint PPT Presentation

3.1. Using and Expressing Measurements. Using and Expressing Measurements How do measurements relate to science?. 3.1. Using and Expressing Measurements. A measurement is a quantity that has both a number and a unit.

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3.1

Using and Expressing Measurements
• Using and Expressing Measurements
• How do measurements relate to science?

3.1

Using and Expressing Measurements
• A measurement is a quantity that has both a number and a unit.
• it is important to be able to make measurements and to decide whether a measurement is correct.
Scientific Notation
• Scientific Notation Pre-Test
Scientific Notation
• 210, 000,000,000,000,000,000,000
• This number is written in decimal notation. When numbers get this large, it is easier to write it in scientific notation
• Where is the decimal in this number?

210, 000,000,000,000,000,000,000.

• Decimal needs moved to the left between the 2 and the 1 ( numbers that are between 1-10)
• When the original number is more than 1 the exponent will be positive.
• 2.1 x 1023
• Exponents show how many places decimal was moved

Express 4.58 x 106 in decimal notation

• Remember the exponent tells you how many places to move the decimal. The exponent is positive so the decimal is moved to the right
• 4,580, 000

express the number 0.000000345 in scientific notation.

• Decimal moved between first 2 non-zero digits and will be moved 7 times
• 3.45 x 10 -7
• The exponent is negative because the original number is a very small number
• 1. 74171.7 2. .07882
• 3. 526 4. .0000573
• 5. 5.8 x 10 -7 6. 5.256 x 106

3.1

Accuracy, Precision, and Error
• Accuracy, Precision, and Error
• What is the difference between accuracy and precision?

3.1

Accuracy, Precision, and Error
• Accuracy and Precision
• Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured.
• Precision is a measure of how close a series of measurements are to one another.

3.1

Accuracy, Precision, and Error
• To evaluate the accuracy of a measurement, the measured value must be compared to the correct value.
• To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.

3.1

Accuracy, Precision, and Error
• Determining Error
• The accepted (Known) value is the correct value based on reliable references.
• The experimental value is the value measured in the lab.
• The difference between the experimental value and the accepted value is called the error.

3.1

Accuracy, Precision, and Error
• The percent error is the absolute value of the error divided by the accepted value, multiplied by 100%.

Experimental – known

3.1

Accuracy, Precision, and Error
• Percent Error
• (Error) 3.00-measurement X 100
• 3.00

3.1

Accuracy, Precision, and Error
• Just because a measuring device works, you cannot assume it is accurate. The scale below has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate.

% ERROR

• The density of aluminum is known to be 2.7 g/ml. In the lab you calculated the density of aluminum to be 2.4 g/ml. What is your percent error?
• What is 5.256X10-6 in standard format
• What is 118000 in scientific notation

3.1

Significant Figures in Measurements
• All measurement contains some degree of uncertainty.
• The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated.
• Measurements must always be reported to the correct number of significant figures
• Using pages 66-72 – fill in your notes regarding the rules of significant figures
Counting Significant Figures

Number of Significant Figures

• 38.15 cm 4
• 5.6 ft 2
• 65.6 lb ___
• 122.55 m ___
• Complete: All non-zero digits in a measured number are (significant or not significant).

Timberlake lecture plus

Number of Significant Figures

• 0.008 mm 1
• 0.0156 oz 3
• 0.0042 lb ____
• 0.000262 mL ____
• Complete: Leading zeros in decimal numbers are (significant or not significant).

Timberlake lecture plus

Sandwiched Zeros

Number of Significant Figures

• 50.8 mm 3
• 2001 min 4
• 0.702 lb ____
• 0.00405 m ____
• Complete: Zeros between nonzero numbers are (significant or not significant).

Timberlake lecture plus

Trailing Zeros

Number of Significant Figures25,000 in. 2

• 200 yr 1
• 48,600 gal 3
• 25,005,000 g ____
• Complete: Trailing zeros in numbers without decimals are (significant or not significant) if they are serving as place holders.

Timberlake lecture plus

Learning Check
• A. Which answers contain 3 significant figures?
• 0.4760 2) 0.00476 3) 4760
• B. All the zeros are significant in
• 1) 0.00307 2) 25.300 3) 2.050 x 103
• C. 534,675 rounded to 3 significant figures is
• 1) 535 2) 535,000 3) 5.35 x 105

Timberlake lecture plus

Significant Figures in Calculations
• A calculated answer cannot be more precise than the measuring tool.
• A calculated answer must match the least precise measurement.
• Significant figures are needed for final answers from

2) multiplying or dividing

Timberlake lecture plus

• The answer has the same number of decimal places as the measurement with the fewest decimal places.
• 25.2one decimal place
• + 1.34two decimal places
• 26.54
• answer 26.5 one decimal place

Timberlake lecture plus

Learning Check
• In each calculation, round the answer to the correct number of significant figures.
• A. 235.05 + 19.6 + 2.1 =
• 1) 256.75 2) 256.8 3) 257
• B. 58.925 - 18.2 =
• 1) 40.725 2) 40.73 3) 40.7

Timberlake lecture plus

Solution
• A. 235.05 + 19.6 + 2.1 =
• 2) 256.8
• B. 58.925 - 18.2 =
• 3) 40.7

Timberlake lecture plus

Multiplying and Dividing
• Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.

Timberlake lecture plus

Multiplication + Division

• Answer should have the same number of significant figures as the measurement with the least.
• You may need to round your answer in order to achieve this
Learning Check
• A. 2.19 X 4.2 =
• 1) 9 2) 9.2 3) 9.198
• B. 4.311 ÷ 0.07 =
• 1)61.582) 62 3) 60
• C. 2.54 X 0.0028 =
• 0.0105 X 0.060
• 1) 11.3 2) 11 3) 0.041

Timberlake lecture plus

Solution
• A. 2.19 X 4.2 = 2) 9.2
• B. 4.311 ÷ 0.07 = 3) 60
• C. 2.54 X 0.0028 = 2) 11 0.0105 X 0.060
• Continuous calculator operation =
• 2.54 x 0.0028  0.0105  0.060

Timberlake lecture plus

3.1

Significant Figures in Calculations
• Rounding
• To round a number, you must first decide how many significant figures your answer should have.
• Your answer should be rounded to the number with the least amount of significant figures
QUIZ
• How many significant figures are in the number
• 603.040 b. 0.0828 c. 690,000

2. Perform the following operations and report to the correct number of sig. figs

• 4.15 cm X 1.8 cm
• 36.47 + 2.721 + 15.1
• 5.6 x 107 x 3.60 x 10-3