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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

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?
slide5

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
slide6

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
slide7

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
slide8
Express the following in scientific notation or standard notation
  • 1. 74171.7 2. .07882
  • 3. 526 4. .0000573
  • 5. 5.8 x 10 -7 6. 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 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.
slide19

% 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 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

leading zeros
Leading Zeros

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
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
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
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) 256.8 3) 257
  • B. 58.925 - 18.2 =
  • 1) 40.725 2) 40.73 3) 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

slide31

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) 11.3 2) 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
slide35
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
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