METRIC AND MEASUREMENTS Scientific Notation Significant Digits Metric System Dimensional Analysis

SCIENTIFIC NOTATION Makes very large or small numbers easy to use Two parts: 1  x < 10 (including 1 but NOT 10) x 10 exponent

WRITING SCIENTIFIC NOTATION EXAMPLES: 1) 2,000,000,000 2) ) ) ) ) 966,666,000 = 2 X 10 9 = 5.43 X 10 3 = 1.23 X = X = 6.00 X = X 10 8 LARGE NUMBERS (>1)POSITIVE EXPONENTS EQUAL TO 1 or itselfZERO EXPONENTS SMALL NUMBERS (<1)NEGATIVE EXPONENTS

WRITING STANDARD FORM EXAMPLES: 1) 4.32 X ) X ) 8.45 X ) X ) X ) 7.00 X = 43,200,000 = = = = 112,300 = POSITIVE EXPONENTSMOVE TO RIGHT NEGATIVE EXPONENTS MOVE TO LEFT

SIGNIFICANT DIGITS Exact numbers are without uncertainty and error Measured numbers are measured using instruments and have some degree of uncertainty and error Degree of accuracy of measured quantity depends on the measuring instrument

RULES 1) All NONZERO digits are significant Examples: a) 543,454,545 b) 34,000,000 Examples: c) 65,945 2) Trailing zeros are NOT significant = 9 = 2 = 5 b) 234,500 = 1 a) 1,000 = 4 c) 34,288,900,000= 6

RULES CON’T 3) Zero’s surrounded by significant digits are significant Examples: a) 1,000,330,134 b) 534,001,000 Examples: c) 7,001,000,100 4) For scientific notations, all the digits in the first part are significant = 10 = 6 = 8 b) 2.34 x = 4a) x 10 9 = 3 c) x = 5

RULES CON’T 5) Zero’s are significant if a) there is a decimal present (anywhere) b) AND a significant digit in front of the zero Zero’s at beginning of a number are not significant (placement holder) Examples: a) b) c) = 3 = 7 = 6 e) = 9d) = 1 f) = 4 g) = 3 = 5h)

Rules for Rounding in Calculations CASE A: In rounding off numbers, the last figure kept should be unchanged if the first figure dropped is less than 5. For example, if only one decimal is to be kept, then becomes 6.4.

CASE B: In rounding off numbers, the last figure kept should be increased by 1 if the first figure dropped is greater than 5 For example, if only two decimals are to be kept, then becomes Similarly, becomes 7.00.

CASE C: In rounding off numbers, if the first figure dropped is 5, and all the figures following the five are zero or if there are no figures after the 5, then the last figure kept should be unchanged if that last figure is even. For example, if only one decimal is to be kept, then becomes 6.6. For example, if only two decimals are to be kept, then becomes 7.48.

CASE D: In rounding off numbers, if the first figure dropped is 5, and all the figures following the five are zero or if there are no figures after the 5, then the last figure kept should be increased by 1 if that last figure is odd. For example, if only two decimals are to be kept, then becomes 6.76.For example, if only two decimals are to be kept, becomes 9.00.

CASE E: In rounding off numbers, if the first figure dropped is 5, and there are any figures following the five that are not zero, then the last figure kept should be increased by 1. For example, if only one decimal is to be kept, then becomes 6.7. For example, if only two decimals are to be kept, then becomes 7.49.

Rounding with 5’s: UP ____ 5 greater than zero = = 34.4  ODD 5 zero = = 101.2

Rounding with 5’s: DOWN  EVEN 5 zero 6.850= = 101.2

CALCULATIONS 1) Multiply and Divide: Least number of significant digits Examples: a) x x 273 b) x 0.14 x x c) / = = x10 10 = e) 150 / 4 = d) x x = 37.5 f) 4.0 x 10 4 x x 10 –3 x x 10 2 = g) 3.00 x 10 6 / 4.00 x = 7.5 x 10 12

CALCULATIONS 2) Add and Subtract: Least precise decimal position Examples: a) = 641.0

ADD AND SUBTRACT CON’T Examples: b) = 1.327

ADD AND SUBTRACT CON’T Examples: c) =

ADD AND SUBTRACT CON’T Examples: d) x = x 10 4

ADD AND SUBTRACT CON’T Examples: e) =

ADD AND SUBTRACT CON’T Examples: f) 1.02 x x x = 1130

MIX PRACTICE Examples: a) = 77.34= b) = = 2.04 c) 1.42 x x x = = 3.8 x 10 2 d) ( x ) 2 = x = x e) ( ) x 4.0 x 10 3 = 9480= 9500

Why the Metric System? International unit of measurement: SI units Base units Derived units Based on units of 10’s

LENGTH Measure distances or dimensions in space Meter (m) Length traveled by light in a vacuum in 1/ seconds.

MASS Measure of quantity of matter Kilogram (kg) Mass of a prototype platinum-iridium cylinder

TIME Forward flow of events Second (s) Time is the radiation frequency of the cesium-133 atom.

VOLUME Amount of space an object occupies Cubic meter (m 3 ) Derived unit 1 mL = 1 cm 3

METRIC PREFIXES PREFIXSYMBOLDEFINITION MEGA-M10 6 = 1,000,000 KILO-k10 3 = 1000 HECTO-h10 2 = 100 DECA-da10 1 = 10 BASE10 0 = 1 DECI-d10 -1 = 0.1 = 1/10 CENTI-c10 -2 = 0.01 = 1/100 MILLI-m10 -3 = = 1/1000 MICRO-μ10 -6 = = 1/1,000,000 NANO-n = = 1/1,000,000,000

DIMENSIONAL ANALYSIS Process to solve problems Factor-Label Method Dimensions of equation may be checked

DIMENSIONAL ANALYSIS Examples: a) 3 years = _______seconds 1 year = 365 days 1 day = 24 hours 1 hour = 60 minutes 1 min = 60 seconds 3 years 1 year 365 days 1 day 24 hours 1 hour 60 minutes 1 minute 60 seconds = seconds= 9 x 10 7 seconds

DIMENSIONAL ANALYSIS Examples: b) mL = ________kL 1 L = 1000 mL 1 kL = 1000 L mL 1000 mL 1 L 1000 L 1 kL = x kL= x 10 –4 kL

DIMENSIONAL ANALYSIS Examples: c) x 10 9 Mg = _________dg 1 Mg = 10 6 g 1 g = 10 dg x 10 9 Mg 1 Mg 10 6 g 1 g 10 dg = x dg

DIMENSIONAL ANALYSIS Examples: d) g OH - = __________ molecules OH - 1 mole = 17 g OH - 1 mole = x molecules g OH - 17 g OH - 1 mole OH x molecules = x molecules = x molecules

DIMENSIONAL ANALYSIS Examples: e) km = __________cm 1 km = 1000 m 1 m = 100 cm km 1 km 1000 m 1 m 100 cm = cm = x 10 6 cm

DIMENSIONAL ANALYSIS Examples: f) 6.7 x seconds = _______years 1 year = 365 days 1 day = 24 hours 1 hour = 60 minutes 1 min = 60 seconds 6.7 x seconds 60 seconds 1 minute 60 minutes 1 hours 24 hours 1 day 365 days 1 year = x years= 2.1 x years

DIMENSIONAL ANALYSIS Examples: g) g He = __________ Liters He 1 mole = 4 g He 1 mole = 22.4 L g He 4 g He 1 mole He 22.4 Liters He = Liters He = Liters He