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Reporting Data in Chemistry: Understanding Significant Figures and Measurement Accuracy

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This guide explores how data should be reported in chemistry, focusing on the distinction between exact numbers and measured numbers, and the concept of significant figures. It covers how to report measurements with estimated digits, evaluate significant figures in scientific notation, and round off numbers correctly. The document includes practical tasks for calculating significant figures, performing arithmetic operations, and emphasizes the importance of accuracy in measurements with tools. Ideal for chemistry students seeking to improve their data reporting skills.

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Reporting Data in Chemistry: Understanding Significant Figures and Measurement Accuracy

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  1. How should data be reported in Chemistry?

  2. There are two kinds of numbers: • Exact numbers: may be counted or defined (they are absolutely accurate).

  3. Numbers obtained from measurements are not exact. These measurements involve estimating.

  4. You can report one estimated digit. • 6.35 or • 6.36 or • 6.37 • the last number is the best estimate for the 3 students. • Two numbers are certain. • One number is uncertain. • three significant figures!

  5. significant figures indicate the uncertainty in measurements

  6. Scientific notation:

  7. How to countsignificant figures ? • 438 g = 4.38 x 102 3 s.f. 2.2678.42 = 2.67842 x 103 6 s.f. 3. 1.7 2 s.f.

  8. Task 1: Try these! A) Write in scientific notation.B) Determine the number of significant figures • 506 • 10.05 • 900.43 • 60.00 • 1.09 • 0.06 • 0.00470

  9. How do you round off? • If the numbers to be discarded are less than 50  leave the last significant number unchanged : 23.31 23 • If the numbers to be discarded are more than 50  add one to the last significant digit : 23.54 24 • If the numbers to be discarded are 50  round off so that the last significant number is an even number : 23.5024

  10. TASK 2: Complete these multiplication and division problems • 13.7 x 2.5 • 200. x 3.58 • 2.3 x 3.45 x 7.42 • 0.003 / 5 • 5. 89 / 9.0 • 6. 5000 / 55 500 = 1 SF 500. = 3 SF 550 = 2 SF On a measuring device, for example the measurement of 500 ml in a measuring cylinder, for the purposes of accuracy this is assumed to be an absolute value.

  11. TASK 3: Complete these addition and subtraction problems • 0.008 + 0.05 • 4.50 + 3 • 35.89 + 34.6 • 200 – 87.3 • 75.0 – 2.55 • 10.0 – 9.9

  12. TASK 4: Apply your knowledge Write: • 35.270 to 3 significant figures • 0.4140 to 2 significant figures • 87.257 to 3 significant figures • 1.350 to 2 significant figures 5. 62.50 to 2 significant figures

  13. Multiple step problems • When carrying out multiple step problems keep one extra significant figure throughout the whole problem, to reduce rounding errors. • The final result should be consistent with the number of significant figures given in the experimental measurements.

  14. Converted, Measured and Counted Numbers • Unit conversions are infinitely accurate. The number of significant figures does not change because conversions are exact values, not measured values. • Counted numbers are infinitely accurate, such as counting the number of atoms in H2O (there are 3). 3 is an exact value not a measured value. Counting does not need a tool. • Measuring requires the use of a tool: ruler, scale, balance, graduated cylinder etc… Measured numbers are only as accurate as the tool being used. The number of significant figures should indicate this.

  15. A great website for practicing Significant figures can be found at: http://www.sciencegeek.net/Chemistry/taters/sigfigs.htm

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