Unit 1B:SCIENTIFIC MEASUREMENT INSTRUCTIONS FOR NOTETAKING: Copy ALL words & examples unless otherwise indicated. Copy NO tables or diagrams unless otherwise indicated. Use Cornell (2-column style) format. Leave room after each EQ for a 3 sentence summary.

Essential Question #4: In what way do significant figures show the inherent uncertainty in measurements? How are significant figures determined in scientific measurements AND calculations?

In every measurement there is a Number followed by a Stating a Measurement In every measurement there is a Number followed by a Unit from a measuring device The number should also be as precise as the measuring device.

Ex: Reading a Meterstick . l2. . . . I . . . . I3 . . . .I . . . . I4. . cm First digit (known) = 2 2.?? cm Second digit (known) = 0.7 2.7? cm Third digit (estimated) between 0.05- 0.07 Length reported = 2.75 cm or 2.74 cm or 2.76 cm

UNITS OF MEASUREMENT Use SI units — based on the metric system Length Mass Volume Time Temperature Meter, m Kilogram, kg Liter, L Seconds, s Celsius degrees, ˚C kelvins, K

Metric Prefixes

Significant Figures (Honors only) The numbers reported in a measurement are limited by the measuring tool Significant figures in a measurement include the known digits plus one estimated digit

Counting Significant Figures: Unlimited Sig Figs (Honors Only) There are 2 instances in which there are an unlimited # of sig figs. Counting. Ex: 23 people in our classroom. Exactly defined quantities. Ex: 1hr = 60 min. Both are exact values. There is no uncertainty. Neither of these types of values affect the process of rounding an answer.

Shortcuts to Sig Figs The Atlantic-Pacific Rule says: "If a decimal point is Present, ignore zeros on the Pacific (left) side. If the decimal point is Absent, ignore zeros on the Atlantic (right) side. Everything else is significant."

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

Significant Numbers in Calculations (Honors Only) A calculated answer cannot be more precise than the measuring tool. A calculated answer must match the least precise measurement. Significant figures are needed for final answers from 1) adding or subtracting 2) multiplying or dividing If you must round to obtain the right # of sig figs, do so after all calcs are complete (“YORO”)

Adding and Subtracting (Honors Only) The answer has the same number of decimal places as the measurement with the fewest decimal places. 25.2 one decimal place + 1.34 two decimal places 26.54 answer 26.5 one decimal place

Learning Check (Honors Only) In each calculation, round the answer to the correct number of significant figures. A. 235.05 + 19.6 + 2.1 = 1) 256.75 2) 256.8 3) 257 B. 58.925 - 18.2 = 1) 40.725 2) 40.73 3) 40.7

Multiplying and Dividing (Honors Only) Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.

Learning Check (Honors Only) A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60 C. 2.54 X 0.0028 = 0.0105 X 0.060 1) 11.3 2) 11 3) 0.041

Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units Example: 1 hr. = 60 min Factors: 1 hr. and 60 min 60 min 1 hr.

How many minutes are in 2.5 hours? Conversion factor 2.5 hr x 60 min = 150 min 1 hr cancel By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

How many seconds are in 1.4 days? Unit plan: days hr min seconds Learning Check How many seconds are in 1.4 days? Unit plan: days hr min seconds 1.4 days x 24 hr x _60min x 60 s = 1 day 1 hr 1 min ANSWER: 120,960 s. FINAL ANSWER (in sig figs) = 120,000 s

Copy one or both of these to your P. Table Density Is the relationship between the MASS of an object and its VOLUME Equation: D = M V Copy one or both of these to your P. Table

How to solve Density Problems Leave room for 2 sample problems. ½ page should suffice.

Temperature Conversions Scientists use 2 Temperature units: Celsius (°C ) & Kelvin (K) Kelvin measures temperature most directly, and MUST be used in certain situations. K = C + 273 Copy this equation to your P. Table

How to Make Temperature Conversions Leave room for 2 sample problems. ½ page will be more than enough.