Using and expressing measurements
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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.

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Using and Expressing Measurements

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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

  • http://www.youtube.com/watch?v=H578qUeoBC0

  • 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


  • Express the following in scientific notation or standard notation

  • 1. 74171.72. .07882

  • 3. 5264. .0000573

  • 5. 5.8 x 10 -76. 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


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.


REVIEW


REVIEW


  • % 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 cm4

    • 5.6 ft2

    • 65.6 lb___

    • 122.55 m___

    • Complete: All non-zero digits in a measured number are (significant or not significant).

    Timberlake lecture plus


    Leading Zeros

    Number of Significant Figures

    • 0.008 mm1

    • 0.0156 oz3

    • 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 mm3

    • 2001 min4

    • 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 yr1

    • 48,600 gal3

    • 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

      1) adding or subtracting

      2) multiplying or dividing

    Timberlake lecture plus


    Adding & Subtracting

    • 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) 256.83) 257

    • B. 58.925 - 18.2 =

    • 1) 40.725 2) 40.733) 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) 11.32) 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

      • 603.040b. 0.0828c. 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


    3.1


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    3.2


    3.3


    3.3


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