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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Using and expressing measurements

3.1

Using and Expressing Measurements

  • Using and Expressing Measurements

    • How do measurements relate to science?


Using and expressing measurements1

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

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

  • Scientific Notation Pre-Test


Scientific notation1

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?


Using and expressing measurements

  • 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


Using and expressing measurements

  • 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


Using and expressing measurements

  • 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


Using and expressing measurements

  • 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


Accuracy precision and error

3.1

Accuracy, Precision, and Error

  • Accuracy, Precision, and Error

    • What is the difference between accuracy and precision?


Accuracy precision and error1

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.


Accuracy precision and error2

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.


Accuracy precision and error3

3.1

Accuracy, Precision, and Error


Accuracy precision and error4

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.


Accuracy precision and error5

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


Accuracy precision and error6

3.1

Accuracy, Precision, and Error

  • Percent Error

  • (Error)3.00-measurement X 100

  • 3.00


Accuracy precision and error7

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


Review1

REVIEW


Using and expressing measurements

  • % 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


Significant figures in measurements

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

    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

    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

    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

    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

    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

    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

    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 check1

    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

    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

    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


    Using and expressing measurements

    • 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 check2

    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


    Solution1

    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


    Significant figures in calculations1

    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


    Using and expressing measurements

    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


    Using and expressing measurements

    3.1


    Using and expressing measurements

    3.1


    Using and expressing measurements

    3.2


    Using and expressing measurements

    3.2


    Using and expressing measurements

    3.3


    Using and expressing measurements

    3.3


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