BELLWORK 9/2/15 How does a scientist reduce the frequency of human error and minimize a lack of accuracy? A. Take repeated measurements B. Use the same method of measurement C. Maintain instruments in good working order. D. All of the above

Why do we have to learn about Sig Figs?

Sig Figs tell you what place to round your answers to. Your final measurement (answer) can never be more precise than your starting measurement. To understand that idea, we will discuss accuracy vs. precision

Two important points in measurement Accuracy & Precision Two important points in measurement

THE BIG CONCEPT Accuracy –indicates the closeness of the measurements to the true or accepted value. Beware of Parallax – the apparent shift in position when viewed at a different angle. 2. Precision - The closeness of the results to others obtained in exactly the same way.

Accuracy vs. Precision High Accuracy High Precision High Precision Low Accuracy

Master Archers

Can you hit the bull's-eye? Three targets with three arrows each to shoot. Accurate and precise Precise but not accurate Neither accurate nor precise How do they compare? Can you define accuracy vs. precision?

Example: Accuracy Who is more accurate when measuring a book that has a true length of 17.0 cm? Susan: 17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm Amy: 15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm

Example - Precision Which set is more precise? A. 18.2 , 18.4 , 18.3 B. 17.9 , 18.3 , 18.8 C. 16.8 , 17.2 , 19.4

Recording Measurements Every experimental measurement has a degree of uncertainty. The volume, V, at right is certain in the 10’s place, 10mL<V<20mL The 1’s digit is also certain, 17mL<V<18mL A best guess is needed for the tenths place.

Known + Estimated Digits In 2.77 cm… Known digits 2 and 7 are 100% certain The third digit 7 is estimated (uncertain) In the reported length, all three digits (2.77 cm) are significant including the estimated one

Always estimate ONE place past the smallest mark! 11.50mL

. l8. . . . I . . . . I9. . . . I . . . . I10. . cm Learning Check What is the length of the line? 1) 9.31 cm 2) 9.32 cm 3) 9.33 cm How does your answer compare with your neighbor’s answer? Why or why not?

Zero as a Measured Number . l3. . . . I . . . . I4 . . . . I . . . . I5. . cm What is the length of the line? First digit 5.?? cm Second digit 5.0? cm Last (estimated) digit is 5.00 cm

Precision and Instruments Do all measuring devices have the same amount of precision?

You indicate the precision of the equipment by recording its Uncertainty Ex: The scale on the left has an uncertainty of (+/- .1g) Ex: The scale on the right has an uncertainty of (+/- .01g)

Below are two measurements of the mass of the same object Below are two measurements of the mass of the same object. The same quantity is being described at two different levels of precision or certainty.

Significant Figures In Measurements

Significant Figures The significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated. The numbers reported in a measurement are limited by the measuring tool.

How to Determine Significant Figures in a Problem Use the following rules:

Rule #1 Every nonzero digit is significant Examples: 24m = 2 3.56m = 3

Rule #2 – Sandwiched 0’s 3 Zeros between non-zeros are significant Examples: 7003m = 4 40.9m = 3

Rule #3 – Leading 0’s Zeros appearing in front of non-zero digits are not significant Act as placeholders Examples: 0. 24m = 2 0.453m = 3

Rule #4 – Trailing 0’s with Decimal Points Zeros at the end of a number and to the right of a decimal point are significant. Examples: 43.00m = 4 1.010m = 4 1.50m = 3

Performing Calculations with Significant Figures Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers. Only count the Sig Figs that come after the decimal.

Adding and Subtracting 2.45cm + 1.2cm = 3.65cm, Round off to  3.7cm 7.432cm + 2cm = 9.432 Round to  9.4cm

Multiplication and Division Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement. Count all of the Sig figs in the entire number.

Examples 75.8cm x 9.6cm = ? 56.78 cm x 2.45cm = 139.111 cm2 Round to  139cm2 75.8cm x 9.6cm = ?

Learning Check State the number of significant figures in each of the following: A. 0.030 m 1 2 3 B. 4.050 L 2 3 4 C. 0.0008 g 1 2 4 D. 3.00 m 1 2 3 E. 2,080,000 bees 3 5 7

Learning Check A. Which answer(s) contain 3 significant figures? 1) 0.4760 2) 0.00476 3) 4760 B. All the zeros are significant in 1) 0.00307 2) 25.300 3) 2.050 x 103 C. 534,675 rounded to 3 significant figures is 1) 535 2) 535,000 3) 5.35 x 105

Learning Check In which set(s) do both numbers contain the same number of significant figures? 1) 22.0 m and 22.00 m 2) 400.0 m and 40 m 3) 0.000015 m and 150,000 m