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Data Recording and Significant Figures

Data Recording and Significant Figures. Data Recording and Significant Figures. Accuracy How close a measurement is to the accepted value. Precision repeatability in measurements. The number of decimal places. For example: 0.1g has less precision than 0.100g. .

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Data Recording and Significant Figures

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  1. Data Recording and Significant Figures Data Recording and Significant Figures

  2. Accuracy How close a measurement is to the accepted value Precision repeatability in measurements. The number of decimal places. For example: 0.1g has less precision than 0.100g. Accuracy and Precision

  3. Recording measurements off of equipment. • estimate one more digit than the equipment provides.

  4. Recording measurements continued • Exception: with electronic equipment, the user is rounding off digits rather than adding them. For example, 2.3456g will be rounded to 2.35g. • Round to nearest .001g.

  5. Using uncertainty in measurements • The estimated digit used when recording data can be written with an uncertainty notation, ± in the measurement. • Example; a graduated cylinder that measures to the nearest ml is used for volume measurements. A student measures 3 different volumes using the same cylinder: 15.5ml, 15.8ml, 15.2ml in an experiment. How would one record these measurements using uncertainty?

  6. Significant Figures • What are significant figures? • They are digits in measurements that were actually measured or estimated in some way. • Numbers that are not measurements are not considered to be significant figures. • Examples are 100 in percent equations, pi, and constants used in scientific equations

  7. Rules for using zeros. • Rule 1: Leading zeros are not significant. These are zeros which precede digits in decimal numbers. • Examples: 0.045g., 0.23 • Rule 2: Captive zeros are significant. These are any zeros that are in between non zero numbers. • Example 2,013, 0.0101, 100.01

  8. Use of zeros continued • Rule 3: Trailing zeros are not significant. These are zeros at the end of large numbers with nodecimal point. • Examples: 100, 10, 2,340 35,000 • Scientific notation is used to remove the trailing zeros. Example: 35,000 becomes 3.50 x 104

  9. Rules for rounding off measurements • Rule 1: when reducing the number of digits, look at the first digit that must be eliminated. • If it ends in a number greater than 5 round up. • If it ends in a number less than 5 round down. • If it ends exactly in 5, round to the nearest even number.

  10. Rules for rounding in calculations • Addition and subtraction • Round off the final answer to the same number of decimal places as the measurement with the fewest decimal places. • Examples. 2.34g + 2.4g + 2.35g=7.09g this should be rounded to 7.1g

  11. Rounding continued • Multiplication and division • The final answer has the same number of significant figures as the measurement with the fewest significant figures. • Example 150.ml x 2.0 x 4.14 = 1242 this must be rounded off to : • 1.2x 103

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