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**Measurements: Accuracy, Precision, & Error**

August 7 & 8, 2014

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How well can I measure this object?

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**Accuracy vs Precision Accuracy Precision**

the extent to which a reported measurement approaches the true value of the quantity measured – how close is the measurement to the reality. Precision the degree of exactness of a measurement (results from limitations of measuring device used).

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**neither accurate nor precise**

Accuracy vs. Precision Example: game of darts precise, not accurate accurate, not precise neither accurate nor precise accurate and precise A B C Which ruler will allow the most precise measurements? Why?

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**neither accurate nor precise**

Accuracy vs. Precision Example: game of darts precise, not accurate accurate, not precise neither accurate nor precise accurate and precise Which ruler will allow the most accurate measurements? Why? A B C Is the most precise instrument always the most accurate instrument? Why or why not?

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Accuracy vs. Precision Another example: Discuss in pairs

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**Errors in Measurement Random Errors**

Measured value can be above OR below the true value with equal probability. Example: normal user error Systematic Errors Due to the system or apparatus Errors are consistently in one direction (always high or always low) Examples: Apparatus calibrated incorrectly Scale not zeroed User making the same error

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Errors in Measurement Turn & Talk with table partner Younger partner … Which type of error would be more common when using a ruler? Describe an example of each type of error with a ruler. Older partner – Which type of error would be more common when using a digital scale? Describe an example of each type of error with a digital scale.

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Significant Figures Can measurements ever be exact? No! Significant figures = reliably known measurements + one estimate 52 mL – reliably known 0.8 – estimate Measurement = 52.8 mL How many significant figures? What is the precision of the measurement? 3 + 0.2 mL

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Significant Figures In table groups … What are the known measurements? What is estimated? What is overall measurement? How many sig figs? 2.6 cm 0.04 cm 2.64 cm 3

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**Significant Figures The simple answer:**

Which numbers in a measurement are significant? The simple answer: all measured & estimated digits are significant all ‘place holders’ are not

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**Significant Figures Which numbers in a measurement are significant?**

All non-zero numbers are significant

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**Significant Figures Which numbers in a measurement are significant?**

All non-zero numbers are significant All zeros between other non-zero digits are significant. (e.g. 503 km)

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**Significant Figures Which numbers in a measurement are significant?**

All non-zero numbers are significant All zeros between other non-zero digits are significant. (e.g. 503 km) Zeros to the left of non-zero digits are not significant (e.g L)

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**Significant Figures Which numbers in a measurement are significant?**

All non-zero numbers are significant All zeros between other non-zero digits are significant. (e.g. 503 km) Zeros to the left of non-zero digits are not significant (e.g L) Zeros to the right of a decimal are significant. (e.g g)

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**Significant Figures Which numbers in a measurement are significant?**

All non-zero numbers are significant All zeros between other non-zero digits are significant. (e.g. 503 km) Zeros to the left of non-zero digits are not significant (e.g L) Zeros to the right of a decimal are significant. (e.g g) Zeros to the right of a non-decimal are ambiguous. Without other info, assume not significant. (e.g m)

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Significant Figures How can you make it obvious whether zeros at the end are significant or not? Use scientific notation! 3000 km Sig figs are ambiguous. 1, 2, 3, or 4? 3.0 X 103 km Sig figs = 2 Alternatively, you can put a line over / under the last significant digit (e.g km)

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Significant Figures How many significant figures? g kg mm mL

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Significant Figures How many significant figures? g 5 sig figs kg 2 sig figs mm 3 sig figs mL 2 sig figs

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Significant Figures Individually, identify the number of significant figures g L m 5080 cm

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Significant Figures Individually, identify the number of significant figures g 5 sig figs L 4 sig figs m 2 sig figs 5080 cm ambiguous – without further info, assume 3 sig figs

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**Calculations with Sig Figs**

When making calculations with measurements, the least precise measurement determines the precision of the final answer.

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**Calculations with Sig Figs**

When making calculations with measurements, the least precise measurement determines the precision of the final answer. Example: If a 5.6 meter flag is placed on top of a 3000 m mountain, how high is the of the flag?

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**Calculations with Sig Figs**

When making calculations with measurements, the least precise measurement determines the precision of the final answer. Example: If a 5.6 meter flag is placed on top of a 3000 m mountain, how high is the of the flag? IT DOESN’T MAKE SENSE TO SAY m.

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**Calculations with Sig Figs**

When adding or subtracting The final answer has the same number of decimals as the least precise measurement.

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**Calculations with Sig Figs**

When adding or subtracting The final answer has the same number of decimals as the least precise measurement. Example: = → 27.2 2.2?? 1.25? 23.894 → you don’t know second decimal in the first measurement and third decimal in second measurement, so the result can not have reliably known second and third decimal.

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**Calculations with Sig Figs**

When adding or subtracting The final answer has the same number of decimals as the least precise measurement. Example: = → 27.2 2.2?? 1.25? 23.894 → IMPORTANT: ROUND AT THE END OF CALCULATIONS

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**Calculations with Sig Figs**

When multiplying or dividing The final answer has the same number of significant figures as the least precise measurement.

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**Calculations with Sig Figs**

When multiplying or dividing The final answer has the same number of significant figures as the least precise measurement. Example: x 5.35 = ( ) = 649 (5 SF) x (3 SF) = = (3SF) Answer should be rounded up to 3 SF only

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**Calculations with Sig Figs**

Do these individually. 4.3 km km + 6 km = 8.23 g – 1.04 g g = 45 mL X 5000 mL = mg ÷ mg =

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**Calculations with Sig Figs**

Do these individually. 4.3 km km + 6 km = 13 km (1s digit) 8.23 g – 1.04 g g = 2.1 g (1 past decimal) 45 mL X 5000 mL = mL (1 sig fig) mg ÷ mg = mg (2 sig figs)

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**Exit Ticket! HW and HW Quiz Closure What were our objectives today,**

and how well did we accomplish them? How did we address our unit statement today? What was our LP trait and how did we demonstrate it?

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