Scientific Measurement Chapter 2 Sec 2.3 Scientific Measurement

What is the measured value? Significant Figures in Measurement all known digits + one estimated digit

Estimating Measurements The hundredths place is somewhat uncertain. Leaving it out would be misleading. Must estimate.. 6.35cm or 6.36cm Probably not EXACTLY 6.35 cm Within .01 cm of actual value. 6.35 cm ± .01 cm 6.34 cm to 6.36 cm

H. Rules of Significant Figures

H. Rules of Significant Figures 1. Every nonzero digit in a measurement is significant (1-9). Ex: 831 g = 3 sig figs 2. Zeros in the middle of a number are always significant. Ex: 507 m = 3 sig figs 3. Zeros at the beginning of a number are NEVER significant. Ex: 0.0056 g = 2 sig figs

H. Rules of Significant Figures 4. Zeros at the end of a number are only significant if a decimal point is present. Ex: 35.00 g = 240. = 2400 g = 00.0350g = 4 sig figs 3 sig figs 2 sig figs

Sig Fig Practice #1 How many significant figures in the following? 5 sig figs 17.10 kg  4 sig figs 100,890 L  5 sig figs These all come from some measurements 3.29 x 103 s  3 sig figs 0.0054 cm  2 sig figs 3,200,000 mL  2 sig figs This is a counted value 5 dogs  unlimited

Sec 2.3 Significant Figures

Sec 2.3 Practice Problems – Significant Figures

I. Significant Figures in Calculations 1. A calculated answer can only be as precise as the least precise measurement from which it was calculated 2. Exact numbers never affect the number of significant figures in the results of calculations (unlimited sig figs) a) counted numbers Ex: 17 beakers b) exact defined quantities Ex: 60 sec = 1min Ex: avagadro’s number = 6.02 x 1023

I. Significant Figures in Calculations 3. multiplication and division: answer can have no more sig figs than least number of sig figs in the measurements used.

I. Significant Figures in Calculations 4. addition and subtraction: a) decimal - answer can have no more decimal places than the least number of decimal places in the measurements used. (not sig figs) b) whole number- answer rounded so final sig fig is in the same place as the leftmost uncertain digit. ex: 5400 + 365 = 5800

Significant Figures, continued Section 3 Using Scientific Measurements Chapter 2 Significant Figures, continued Rounding

Rounding Sig Fig Practice #1 Calculation Calculator says: Answer 3.24 m x 7.0 m 22.68 23 m2 100.0 g ÷ 23.7 cm3 4.219409283 4.22 g/cm3 0.02 cm x 2.371 cm 0.04742 0.05 cm2 710 m ÷ 3.0 s 236.6666667 240 m/s

Rounding Practice #2 Calculation Calculator says: Answer 3.24 m + 7.0 m 10.24 10.2 m 100.0 g - 23.74 g 76.26 76.3 g 0.02 cm +2.378 cm 2.398 2.40 cm 710 m -3.4 m 706.6 707 m

Rounding Practice #3 Calculation Calculator says: Answer 324 m + 70 m 394 390 m 1300 g - 237 g 1063 1100 g 1250 cm + 25 cm 1275 1280cm odd # preceding 5 720 m -35 m 685 680 m even # preceding 5

Rounding Practice #4 Calculation Calculator says: Answer 3.25 m + 0.7 m 3.95 4.0 m odd # preceding 5 1.55 g - 0.3 g 1.25 1.2 g even # preceding 5 21.25 g ÷ 7.2 cm3 2.9513888 3.0 g/cm3 55.00 m x 33.50 m 1842.5 1842 m2

Sec 2.3 Practice Problems – Significant Figures

Sec 2.3 Practice Problems – Significant Figures

Scientific Notation An expression of numbers in the form m x 10n where m (coefficient) is equal to or greater than 1 and less than 10, and n is the power of 10 (exponent)

J. Rules of Scientific Notation 1. Multiplication – multiply the coefficients and add the exponents Ex: (3x104) x (2x102) = (3x2) x 104+2 = 6 x 106 2. Division – divide the coefficients and subtract the exponent in the denominator from the exponent in the numerator Ex: (3.0x105)/(6.0x102) = (3.0/6.0) x 105-2 = 0.5 x 103 = 5.0 x 102

J. Rules of Scientific Notation 3. Addition – exponents must be the same and then add the coefficients Ex: (5.4x103) + (8.0x102) (8.0x102) = (0.80x103) (5.4x103) + (0.80x103) = (5.4 +0.80) x 103 = 6.2 x 103 4. Subtraction – exponents must be the same and then subtract the coefficients Ex: (5.4x103) - (8.0x102) (5.4x103) - (0.80x103) = (5.4 - 0.80) x 103 = 4.6 x 103

Sec 2.3 Practice Problems – Scientific Notation

Chapter 2 Direct Proportions Section 3 Using Scientific Measurements Chapter 2 Direct Proportions Two quantities are directly proportional to each other if dividing one by the other gives a constant value. read as “y is proportional to x.”

Direct Proportion A straight line graph results from the relationship of direct proportion y x = k The line is extrapolated to pass through the origin

Chapter 2 Inverse Proportions Section 3 Using Scientific Measurements Chapter 2 Inverse Proportions Two quantities are inversely proportional to each other if their product is constant. read as “y is proportional to 1 divided by x.”

Inverse Proportion xy = k A graph of variables that are inversely proportional produces a curve called a hyperbola xy = k

Vocabulary 14. accuracy 15. precision 16. percent error 17. significant figures 18. scientific notation 19. directly proportional 20. inversely proportional