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2 4 significant_fig_in_calc

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Transcript

  • 1. Chapter 2 Measurements
    • 2.4
    • Significant Figures in
    • Calculations
    Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  • 2. Rounding Off Answers
    • In calculations
    • answers must have the same number of significant figures as the measured numbers
    • calculated answers are usually rounded off
    • rounding rules are used to obtain the correct number of significant figures
    Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  • 3. Rounding Off Calculated Answers
    • When the first digit dropped is 4 or less , the retained numbers remain the same.
    • to round off 45.832 to 3 significant figures
    • drop the digits 32 = 45.8
    • When the first digit dropped is 5 or greater , the last retained digit is increased by 1.
    • to round off 2.4884 to 2 significant figures
    • drop the digits 884 = 2.5 ( increase by 0.1)
    Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  • 4. Adding Significant Zeros
    • Sometimes a calculated answer requires more significant digits. Then one or more zeros are added .
    • Calculated Zeros Added to
    • Answer Give 3 Significant Figures
    • 4 4.00
    • 1.5 1.50
    • 0.2 0.200
    • 12 12.0
    Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  • 5. Learning Check
    • Adjust the following calculated answers to give
    • answers with three significant figures:
    • A. 824.75 cm
    • B. 0.112486 g
    • C. 8.2 L
    Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  • 6. Solution
    • Adjust the following calculated answers to give
    • answers with three significant figures:
    • A. 825 cm first digit dropped is greater than 5
    • B. 0.112g first digit dropped is 4
    • C. 8.20 L significant zero added
    Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  • 7. Calculations with Measured Numbers
    • In calculations with measured numbers, significant figures or decimal places are used to determine the correct number of figures in the final answer.
    Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  • 8.
    • When multiplying or dividing , use
    • the same number of significant figures (SFs) as in the measurement with the fewest significant figures
    • rounding rules to obtain the correct number of significant figures
    • Example
    • 110.5 x 0.048 = 5.304 = 5.3 (rounded)
    • 4 SFs 2 SFs calculator 2 SFs
    Multiplication and Division Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  • 9.
    • Give an answer for each with the correct
    • number of significant figures.
    • A. 2.19 x 4.2 =
    • 1) 9 2) 9.2 3) 9.198
    • B. 4.311 ÷ 0.07 =
    • 1) 61.59 2) 62 3) 60
    • C. 2.54 x 0.0028 =
    • 0.0105 x 0.060
    • 1) 11.3 2) 11 3) 0.041
    Learning Check Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  • 10.
    • 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
    • On a calculator, enter each number followed by
    • the operation key.
    • 2.54 x 0.0028  0.0105  0.060 = 11.28888889
    • = 11 ( rounded off )
    Solution Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  • 11.
    • When adding or subtracting , use
    • the same number of decimal places as the measurement with the fewest decimal places
    • rounding rules to adjust the number of digits in the answer
    • 25.2 one decimal place
    • + 1.34 two decimal places
    • 26.54 calculated answer
    • 26.5 final answer (one decimal place)
    Addition and Subtraction Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  • 12.
    • For each calculation, round the answer to give
    • the correct number of digits.
    • A. 235.05 + 19.6 + 2 =
    • 1) 257 2) 256.7 3) 256.65
    • B. 58.925 - 18.2 =
    • 1) 40.725 2) 40.73 3) 40.7
    Learning Check Basic Chemistry Copyright © 2011 Pearson Education, Inc.
  • 13.
    • A. 235.05 hundredths place (2 decimal places)
    • +19.6 tenths place (1 decimal place)
    • + 2 ones place
    • 256.65 rounds to 257 answer (1)
    • B. 58.925 thousandths place (3 decimal places)
    • -18.2 tenths place (1 decimal place)
    • 40.725 round to 40.7 answer (3)
    Solution Basic Chemistry Copyright © 2011 Pearson Education, Inc.