MEASUREMENTS Kenneth E. Schnobrich

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

NORMAL MEASUREMENTS LENGTH 2. MASS TIME 4. TEMPERATURE

Interval between 2 events 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 Length Mass Time Temperature

BASIC vs DERIVED Derived Units are combinations of the basic units Area L x W Volume L x W x H Density Mass/Volume Energy Joule (kg•m2/s2) or calorie Pressure Pa = kg/m•s2

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

COMMON PREFIXES Prefix Symbol Meaning Exp. Not. Mega M 1,000,000. 106 Kilo k 1,000. 103 Hecto h 100. 102 Deca D 10. 101 Deci d 0.1 10-1 Centi c 0.01 10-2 Milli m 0.001 10-3 Micro µ 0.000001 10-6 Nano n 0.00000001 10-9

UNIT CONVERSIONS Convert 25.4 kg to g: Convert 8500 m to mm: 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 are 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: All digits in a measurement are considered significant Zeros that fall between digits are considered significant Zeros to the right of a decimal and to the left of a non-zero are considered significant If a decimal point is placed after a zero all of the intervening zeros are significant 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: 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 3.2 5.0043 1.02 4.02 13.3

EXAMPLES Multiplying and Dividing 4.91 5.0043 4.032 1.02 5.0043 20.33

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: 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