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Significant Digits

Significant Digits

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Significant Digits

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  1. Significant Digits Uncertainty of Measurement

  2. Three Rules • Non-zero digits are significant • Zeros between two significant digits are significant • Zeros at the right end of a number, after a decimal point, are significant

  3. Number 455.6 7.98 0.6224 5.2 Significant Digits 4 3 4 2 Non-zero digits are significant

  4. Zero to left of decimal point • 0.78895 5 significant digits • The zero to the left of the decimal point is there to communicate that the decimal point is a decimal point - convention

  5. Problems! • Numbers like 308.5 0.000811 5000

  6. Number 28.09 1008.91 3.005 2.03 Significant Digits 4 6 4 3 Zeros between non-zero digits are significant

  7. Space Holding zeros on numbers less than one • 0.00678 3 significant digits • 0.030086 5 significant digits

  8. Trailing Zeros • 200 is considered to have only one significant digit • 38,000 has two significant digits

  9. Problem area • 5000 might really have four significant digits - an exact count or measurement • write number as 5000. • Scientific notation used to indicate significant digits

  10. 78002.1 0.00006003 34.61 8.81 42,300 6 4 4 3 3 Review

  11. Multiplication & Division • An answer cannot have more significant digits than the measurement with the least number of significant digits used in the operation. (3.006) X (0.0067) = 0.0201402 = 0.020 only 2 sig. Digits

  12. Addition & Subtraction • The answer is rounded to the least number of places in the decimal portion of any number in the operation 134.008 89.70 57.9 281.608 = 281.6