Scientific Measurement Ch. 3

Scientific Notation 3-1

Qualitative vs. Quantitative –Qualitative observations – descriptions of the quality of the object or its physical appearance (examples: oval, square, round, cold, hard, salty) –Quantitative observations – numbers or amounts that describe the object (examples: 3 inches wide, 2.5 grams, 98.6  F)

The room is cold would be a A)Qualitative observation B)Quantitative observation C)Precise observation D)All of the above

Scientific Notation Way to express numbers through the power of 10 Powers of 10: 10 0 = = = 10x = 10x10x10 Goal: express large and small numbers in a single digit Example: –3500 becomes –3.5 x 10 x 10 x10 –3.5 x 10 3

Scientific Notation Short cut: –Count the number of spaces you move left or right until decimal falls just after first nonzero digit –3500 to 3.5 is 3 jumps left –For each jump left add a positive exponent on the 10. –For each jump right add a negative exponent on the 10 –So 3500 is now 3.5 x 10 3

Let’s Try! Convert to scientific notation: x ,000,000 8 x x Convert to normal: 1.6 x x x x  When converting back to normal, jump the decimal the opposite way. -For positive exponent, jump right (make # bigger) -For negative exponent, jump left (make # smaller)

Scientific Notation when Multiplying + Dividing When multiplying, add the powers of 10 Ex: (4.5 x )(3.0 x 10 8 ) = (4.5 x 3.0) x = 13.5 x = 1.35 X When dividing, subtract the powers of 10 Ex:4.5 x x 10 8 = 1.5 x 10 (12-8) = 1.5 x 10 4

Addition/Subtraction in Scientific Notation Before adding or subtracting in scientific notation, you need to make the exponents the same in both numbers. (5.40 x 10 3 ) + (6.3 x 10 3 ) = ( ) x 10 3 = 11.7 x 10 3 = 1.17 x 10 4

Let’s Try! (4x10 7 ) x (2x10 -3 ) = (4x2) x 10 7+(-3) = 8x10 4 (6.3x10 -2 ) / (2.1x10 4 ) = (6.3/2.1) x = 3.0x10 -6 (4.6x10 3 ) – (1.8x10 3 ) = ( ) x 10 3 = 2.8x10 3

Significant Figures + Uncertainty in Measurements 3-2

Significant Figures Used for accurate measurements Meaningful digits are significant figures (sig figs). Rules: 1.All nonzero digits are significant (1-9) Ex: g____ # of sig figs 2.Zeros occurring in the middle are significant Ex: 56.06g____ # of sig figs 3.Zeros to the right (trailing), if there is a decimal point, are significant Ex: 73.00g____ # of sig figs 4.Zeros to the right (trailing), with NO decimal point, are NOT significant Ex: 100g ____ # of sig figs 5.Zeros to the left (beginning) of the first nonzero digit are NOT significant Ex: 0.09g____ # of sig figs

Let’s Try! How many sig figs? –0.0672mL 3 –1.526g 4 –0.10mg 2 –607mm 3 – Round to 2 sig figs: –0.0672mL 0.067mL –1.526g 1.5g –0.10mg 0.10mg –536, ,000 Rounding: If > 5 round up If < 5 stays same

More Sig Figs (College Prep only, Concept cross out) Addition/Subtraction: –The answer has only as many decimal places as the measurement having the least # of decimal places. –Ex: 190.2g g g = g Round to tenths place 267.9g Multiplication/Division: –The answer has only as many sig figs as the measurement with the least # of sig figs. –Ex: 13.78g/11.3mL = g/mL Round to 3 sig figs 1.22g/mL

(College Prep ONLY) Addition or Subtraction The limiting term is the one with the smallest number of decimal places to the right Round off 21.1

(College Prep ONLY) Multiplying or Dividing The limiting term is the one with the fewest number of sig figs x 18.0 = Round off218

You Try! (College Prep ONLY) What is the answer in the correct sig figs? 7.55m x 0.34m = 2.567m 2 2.6m m m = m 46.29m

MEASUREMENT in LAB Always Estimate the last place. 1 cm 2 cm 1.85 or 1.84 cm While the last number is uncertain, it is more accurate than rounding to 1.8 cm

READING A RULER

Accuracy, Precision and Error Accuracy is the measure of how close a measurement comes to the actual or true value Precision is the measure of how close a series of measurements are to one another Error is the difference between the accepted value and the experimental value.

Precision vs Accuracy no noThe first bulls-eye has no precision and no accuracy. noThe second bulls-eye has precision but no accuracy. The third bulls-eye has precision and accuracy. In a lab setting, which outcome is most desirable?

Calculating Percent Error Accepted value = correct value based on reliable references Experimental value = value measured in lab. Percent error = [accepted - experimental] x 100 accepted value Ex: [100°C – 99.1°C] x °C = 0.9% error

Calculator Input (not in notes) Find button: EE, EXP, x10, x10 n, x10 x (DON’T use 10 x or ∧ ) These buttons mean “x10” with one press To input (3.2x10 6 ) x (6.8x10-3) type: 3.2 EE 6 x 6.8 EE -3 = Try (8.99x10 4 ) / (6.5x ) 8.99 EE 4 / 6.5 EE -23 = 1.383x10 27

Calculator Input (not in notes) Put calculator in scientific notation: –Find “mode,” should see “norm or flo, sci, ….” among other options. Put it in “sci” –Try 9.5 x 6225 –Should get “ x10 4 ” NOT “ ” Take calculator out of scientific notation: –Find “mode,” put back in “norm or flo” –Try 9.5 x 6225 again –Should get “ ” NOT “ x10 4 ”

Calculator Input (not in notes – College Prep only) Try: (6.25x10 24 ) (8.3x10 3 ) (1.6x10 -5 ) (1.92x10 3 ) (6.7x10 15 ) = 6.5x10 4 Try: 3.21x10 -3 x 2.6x10 4 x 2.9x x x10 9 = 2.6x10 4

International System of Units 3-3

Measurement Scientists use the International System of Units, or SI. –Required to keep measurement consistent Length in meter (m) Mass kilogram (kg) Volume in cubic meters (m 3 ) Temperature in Kelvin (K) Energy in Joules (J)

DRAW!

Let’s Try Metrics 1250 m = _____ km –1.25km 5.6 kg = _____ g –5600g 16 cm = _____ mm –160mm 120 mg = ____ g –0.12g Use, = (College Prep only) 5 g ____ 508 mg 5 g > g 3.6 m ____ 36 km 3.6 m < 36,000 m

Mass vs. Weight Mass is the amount of matter that makes up an object. Weight is a measure of the force of gravity on an object Weight changes based on location, mass does NOT change.

Volume Volume is the amount of space contained in an object Volume of a box = length x width x height, with the unit cm 3 V = l x w x h Water: 1 cm 3 = 1 mL = 1 g = L Volume of object not box shaped: use water displacement

Ex: –fill graduated cylinder with 200mL (cm3) of water –Drop in a penny –Water level increases to 270mL –How much volume does the penny have? 270mL – 200mL = 70mL! Water Displacement

Density 3-4

Density Density is the amount of matter (mass) compared to the amount of space (volume) the object occupies. Units in g/cm 3 or g/mL Calculate using formula or wheel Ex: D = ? m = 10 g v = 2 mL D = 5 g/mL Ex: m = ? D = 12 g/cm 3 v = 2 cm 3 m = 24 g Mass DensityVolume D = m v m = D*v v = m D

Which substance is the densest? honey Which substance is the least dense? lamp oil

Temperature 3-5

Measuring Temperature Celsius scale: water freezes at 0°C, boils at 100°C Kelvin scale: water freezes at 273K, boils at 373K Absolute zero = 0 K = -273 °C Conversion: K = °C °C = K – 273 If it is 37 °C, what K is it? K = 37 °C = 310K