MEASUREMENTS Kenneth E Schnobrich WHAT DO WE HAVE

MEASUREMENTS Kenneth E. Schnobrich

WHAT DO WE HAVE TO DO? 1. WE MUST DEFINE WHAT IT IS WE ARE GOING TO MEASURE 2. WE MUST ESTABLISH A STANDARD 3. WE MUST DEVELOP SOMETHING TO COMPARE TO THE STANDARD

NORMAL MEASUREMENTS 1. LENGTH 2. MASS 3. TIME 4. TEMPERATURE

TYPICAL UNITS UNIT DEFINITION STD COMPARE LENGTH Dist. Between 2 points Meter Metric rule MASS Quantity of matter grams or kilograms Balance TIME Interval between 2 events Second Timer/clock TEMP. Measure of avg. K. E. °C or K thermometer

BASIC vs DERIVED Basic Units or Fundamental Units are those we just mentioned 1. Length 2. Mass 3. Time 4. Temperature

BASIC vs DERIVED Derived Units are combinations of the basic units 1. Area Lx. W 2. Volume Lx. Wx. H 3. Density Mass/Volume 4. Energy Joule (kg • m 2/s 2) or calorie 5. Pressure Pa = kg/m • s 2

WHY THE METRIC SYSTEM? • BASED ON DIVISIONS OF OR MULTIPLES OF TEN • THERE ARE COMMON PREFIXES • THE SYSTEM IS WIDELY ACCEPTED

COMMON PREFIXES Prefix Mega Kilo Hecto Deca Deci Centi Milli Micro Nano Symbol M k h D d c m µ n Meaning Exp. Not. 1, 000. 106 1, 000. 103 100. 102 10. 101 0. 1 10 -1 0. 01 10 -2 0. 001 10 -3 0. 000001 10 -6 0. 00000001 10 -9

UNIT CONVERSIONS Convert 25. 4 kg to g: 25. 4 kg x (1000 g/kg) = 25400 g Convert 8500 m to mm: 8500 m x (1000 mm/m) = 8500000 mm

WHAT IS A SIGNIFICANT FIGURE? When you are making a measurement there always a certain number of known or certain digits. Then as part of the measurement there will always be a digit that is uncertain because it is your guess. The known or certain digits plus the first unknown Digit are referred to as the SIGNIFICANT FIGURES

PRECISION vs ACCURACY PRECISION: this refers to a situation where the same result is gotten each time you perform the operation • repeatedly hitting the same spot in darts ACCURACY: this refers to how close you come to the accepted value or result • how close you are to the bullseye

SIGNIFICANT FIGURES The following rules apply to significant figures: 1. All digits in a measurement are considered significant 2. Zeros that fall between digits are considered significant 3. Zeros to the right of a decimal and to the left of a non -zero are considered significant 4. If a decimal point is placed after a zero all of the intervening zeros are significant 5. Zeros after a digit but not followed by a decimal are not significant

EXACT NUMBERS These are usually numbers that are obtained by counting rather than using a measuring device such as a buret or graduated cylinder - 12 eggs in a dozen, 2 socks in a pair, 144 things in a gross

SIGNIFICANT FIGURES Working with Significant figures: 1. When you add or subtract numbers: the final answer can have no more decimal places than the least precise value in the operation 2. When you multiply or divide numbers: the final answer can have no more significant figures than the smallest number of significant figures in the operation

EXAMPLES ADDING & SUBTRACTING: 5. 0043 4. 032 1. 02 4. 02 3. 2 13. 3

EXAMPLES Multiplying and Dividing 5. 0043 4. 032 20. 33 4. 91 1. 02 5. 0043

MORE EXAMPLES How many Significant figures in each of the following: 1. 0. 0043 2. 1. 0043 3. 14300 4. 5820. 5. 30089 6. 2. 0607

MORE EXAMPLES How many Significant figures in each of the following: 1. 243. 0 x 1. 8 = 2. 1. 0043 + 2. 08 = 3. 14300/4 = 4. 5820. x 4. 32 = 5. 30089 - 7. 32 = 6. 2. 0607 + 3. 85 =

ROUNDING When rounding use only the first digit to the right of the last significant figure. 4. 348 becomes 4. 3 if rounded to 2 sig. figs. Rules: -In a series of calculations, carry the extra digits through to the final result, then round. -If the digit to be removed -Is less than 5 the preceding digit stays the same. 1. 33 becomes 1. 3 -Is equal to or greater than 5, the preceding digit is increased by 1. 1. 36 becomes 1. 4