# Measurement vs. Number Significant Digits and Accuracy Exact numbers – number determined by counting or definition Approximate numbers – number determined.

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Measurement vs. Number

Significant Digits and Accuracy Exact numbers – number determined by counting or definition Approximate numbers – number determined by measurement or estimation

Accuracy Accuracy – number of digits we are reasonably sure of having counted (all certain digits + 1 st uncertain) Called significant digits The greater the number of significant digits, the better the accuracy For our graduated cylinder, accuracy is to 3 significant digits 1 2 3

Accuracy/Sig Fig Example These divisions were visualized Reading is between 2.8 cm & 2.9 cm 2.85 cm is measurement “5” is uncertain

Significant Figures Includes all numbers recorded in a measurement  For pin, length = 2.85 cm: 3 significant figures  All certain numbers plus first uncertain Assume to be accurate to ± 1 in last #  Pin length is 2.85 ± 0.01 cm  Pin is somewhere between 2.84 & 2.86 cm

Accuracy & Sig Figs All of the following have 2 significant figures 3863.8638.60.386 0.0386386003860386000 All of the following have 3 significant figures 414.10.410.041 410410041000410000

Precision Precision – smallest unit with which measurement is made, or the position of the last significant digit Try not to confuse accuracy and precision (often have similar meanings) Which measuring instrument is more precise?

Precision of Numbers All of the following are precise to 0.01 0.525.2052.0052.02520.00 0.050.0225.2025.022.05 All of the following are precise to 100 52002005005250050500 1235001200450060098700

Accuracy vs. Precision

Which Number is most Precise? 8638.6386.3 Which Number is most Accurate? 88.686.3

Accuracy & Precision of Data ReplicatesResults 110.28 210.22 39.81 49.75 510.36 69.76 710.11 89.86 910.25 109.86 Average10.03 Standard Deviation 0.24 True Value = 10.00 Accuracy = Good (Average = 10.03) Precision = Bad (Std Dev = 0.24)

Accuracy & Precision of Data ReplicatesResults 110.56 210.51 310.55 410.49 510.36 610.59 710.38 810.60 910.59 1010.53 Average10.52 Standard Deviation 0.08 True Value = 10.00 Accuracy = Bad (Average = 10.52) Precision = Good (Std Dev = 0.08)

Accuracy & Precision of Data ReplicatesResults 110.03 210.05 39.97 410.01 510.11 69.95 79.98 810.02 99.96 1010.03 Average10.01 Standard Deviation 0.04 True Value = 10.00 Accuracy = Good (Average = 10.01) Precision = Good (Std Dev = 0.04)

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