Measurement Significant Figures Precision and Accuracy Low Accuracy

• Slides: 14

Measurement: Significant Figures

Precision and Accuracy Low Accuracy High Precision High Accuracy Low Precision High Accuracy High Precision

Significant Figures o Significant Figures (sig. figs. ): the number of digits that carry meaning contributing to the precision of a measurement or calculated data.

Significant Figures o The significance of a digit has to do with whether it represents a true measurement or not. o Any digit that is actually measured or estimated will be considered significant. o Placeholders, or digits that have not been measured or estimated, are not considered significant.

Significant Figures o There are 5 rules to determine which digits in a measurement or number are significant or not.

Rules for Significant Figures o Rule #1: All non-zero digits (1 -9) are significant. For example: 453 number of sig figs______ 345. 21 number of sig figs______

Rules for Significant Figures o Rule #2: Zeros between non-zero digits are significant. For example: 12. 007 number of sig figs______ 3008007 number of sig figs______

Rules for Significant Figures o Rule #3: Zeros to the left (“leading” zeros) of the first non-zero digit are NOT significant. For example: 1. 02 0. 12 0. 00127 0. 00040301 number of sig figs______ number of sig figs______

Rules for Significant Figures o Rule #4: If a number ends in zeros (“lagging” zeros) to the right of the decimal point, those zeros are significant. For example: o 2 number of sig figs______ 2. 0 number of sig figs______ 2. 00 number of sig figs______ 2. 000 number of sig figs______ {This signifies greater precision. }

Rules for Significant Figures o Rule #5: If a number ends in zeros (“lagging” zeros), the zeros to the right are NOT significant IF there is NO decimal point present. For example: 47100 number of sig figs______ 20060 number of sig figs______ 40000 number of sig figs______

Sig. Figs. Practice Ex 1) 0. 020110 Ex 2) 730800 n 1) 48001 n 2) 9807000 n 3) 0. 008401 n 4) 40. 500 n 5) 64000 n 6) 64000. n 7) 64000. 00 n 8) 0. 0107050 Ex 1) 0. 020110 (5 sig. figs. ) Ex 2) 730800 (4 sig. figs) n 1) 48001 (5 sig. figs. ) n 2) 9807000 (4 sig. figs. ) n 3) 0. 008401 (4 sig. figs. ) n 4) 40. 500 (5 sig. figs. ) n 5) 64000 (2 sig. figs. ) n 6) 64000. (5 sig. figs. ) n 7) 64000. 00 (7 sig. figs. ) n 8) 0. 0107050 (6 sig. figs. )

Calculations with Sig Figs o Add and subtract: o Example: o Answer gets o 334. 540 + rounded based on 198. 9916 the fewest o 533. 6316 decimal places o The last 6 isn’t from question significant because the fewest decimal places in the Q is the third

Calculations with Sig Figs o Multiply and o 44 x 20 = 880 Divide: o Round to 900 o Answer gets because one of rounded to fewest the values in the significant figures question only has from the question one sig fig

Answers to Significant Figure Calculation Practice o 1) 533. 532 g o 2) 3. 4 g/ml o 3) o 4) -0. 12 m o 5) 450. cm o 6) 0. 28 m/s o 7) 332. 107 kg o 8) 900 m