Units and Measurement Physical Science

Measurement How tall are you? How tall are you? How old are you? How old are you? A number without a unit is meaningless A number without a unit is meaningless

Metric System Metric System Measurements have two parts Measurements have two parts Base unit and prefix Base unit and prefix Prefixes different by factors of 10 Prefixes different by factors of 10 Prefixes are the same for all units Prefixes are the same for all units SI – International System SI – International System

Base SI Units Base SI Units QuantityUnitSymbol Lengthmeterm Masskilogramkg TemperaturekelvinK Timeseconds Amount of Substance molemol Electric CurrentampereA Base SI Units (examples)

Derived SI Units (examples) QuantityunitSymbol Volumecubic meterm3m3 Densitykilograms per cubic meter kg/m 3 Speedmeter per secondm/s Newtonkg m/ s 2 N EnergyJoule (kg m 2 /s 2 )J PressurePascal (kg/(ms 2 )Pa

SI Unit Prefixes NameSymbol giga-G10 9 mega-M10 6 kilo-k10 3 NO PREFIX10 0 deci-d10 -1 centi-c10 -2 milli-m10 -3 micro-μ10 -6 nano-n10 -9

Centimeters and Millimeters

Conversion Factors 1 meter (m) = 100 centimeters (cm) 1 meter (m) = 100 centimeters (cm) 1 kilometer (km) = 1000 meters (m) 1 kilometer (km) = 1000 meters (m) 1 centimeter (cm) = 10 millimeters (mm) 1 centimeter (cm) = 10 millimeters (mm) 1 meter (m) = 1000 millimeters (mm) 1 meter (m) = 1000 millimeters (mm)

Factor-Label Method of Unit Conversion Example: Convert 5km to m: Example: Convert 5km to m: NEW UNIT NEW UNIT 5km x 1,000m =5,000m km OLD UNIT OLD UNIT

Factor-Label Method of Unit Conversion: Example Example: Convert 7,000m to km Example: Convert 7,000m to km 7,000m x 1 km =0.007m 7,000m x 1 km =0.007m 1,000m 1,000m

Practice Problems Handout from class Handout from class

Scientific Notation M x 10 n M is the coefficient 1<M<10 M is the coefficient 1<M<10 10 is the base 10 is the base n is the exponent or power of 10 n is the exponent or power of 10

1)Put the decimal after the first non- zero digit. Example: To convert 5,668,000 first write Example: To convert 5,668,000 first write To write a number to scientific notation:

2) To find the exponent count the number of places from the decimal to the end of the original number. In there are 6 places after the decimal. So the exponent is 6 or 10 6

3) Drop the ending (or beginning) zeros (if any). So 5,668,000 is written as: 5.668x x10 6

Scientific Notation Exponents are often expressed using other notations. Exponents are often expressed using other notations E+6 or 5.668E+6 or x 10^ x 10^6

Numbers less than 1 will have a negative exponent. Numbers less than 1 will have a negative exponent. A millionth of a second is: A millionth of a second is: sec 1x E-6 1.0^-6 1.0E-6 1.0^-6

Example 1 Express the following in scientific notation: 73,822 m= g= 34, s= m=

Example 2 Express the following in standard numerical form: Express the following in standard numerical form: 4.75 x m= 8.99 x 10 7 g= 1.44 x 10 1 s= x m=

Problem Solving Method 1) Make a list of: knowns unknowns 2) a) If applicable, make a diagram. b) Write the related formula. b) Write the related formula. c) Substitute the numbers with units and check that the units are uniform. c) Substitute the numbers with units and check that the units are uniform. 3) Write the answer with the units.

Division in Scientific Notation New coefficient= quotient of coefficients New coefficient= quotient of coefficients New exponent= exponent of numerator -exponent of denominator New exponent= exponent of numerator -exponent of denominator Perform the following calculations: Perform the following calculations: 12 x 10 2 kg / 8 x 10 2 m 3 = 24 x 10 4 kg/ 6 x 10 2 m 3 =

Addition and Subtraction in Scientific Notation A. First express each number with the same exponent as the other B. New coefficient=sum of coefficients Perform the following calculations: 3 x x 10 4 = 5 x x = 1.5 x x 10 3 =

Limits of Measurement Accuracy and Precision Accuracy and Precision

Accuracy - a measure of how close a measurement is to the true value of whatever is being measured. Accuracy - a measure of how close a measurement is to the true value of whatever is being measured.

Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is. Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.

Precision versus Accuracy

Example: Evaluate whether the following are precise, accurate or both. Accurate Not Precise Not Accurate Precise Accurate Precise

Example: Precision Who is more precise when measuring the same 17.0cm book? Susan: Susan: 17.0cm, 16.0cm, 18.0cm, 15.0cm 17.0cm, 16.0cm, 18.0cm, 15.0cmAmy: 15.5cm, 15.0cm, 15.2cm, 15.3cm

Measuring length Use a ruler (metric side) Use a ruler (metric side) Line up from zero not the end of the ruler Line up from zero not the end of the ruler Small divisions are millimeters Small divisions are millimeters 01234

Measuring Volume Use a graduated cylinder. Use a graduated cylinder. The water will curve in the cylinder. The water will curve in the cylinder. Hold it level with your eye. Hold it level with your eye. Read the bottom of the curve. Read the bottom of the curve. Measures in milliliters mL. Measures in milliliters mL

Measuring Mass Use a triple beam balance Use a triple beam balance First balance it at zero. First balance it at zero. Then put item on Then put item on Then move one weight at a time Then move one weight at a time When balanced, add up the weights When balanced, add up the weights

Graphs Give a visual representation of data Give a visual representation of data Two types of variables Two types of variables Independent variable the thing you have control over Independent variable the thing you have control over Dependent variable the thing that you don’t have control over. Dependent variable the thing that you don’t have control over.

Line Graphs Line Graphs- compares sets of data, show change and patterns over time. Line Graphs- compares sets of data, show change and patterns over time.

Slope = Rise/Run Slope = Rise/Run Direct Proportion – relationship in which the ratio of two variables is constant Direct Proportion – relationship in which the ratio of two variables is constant Inverse proportion – relationship in which the product of two variables is constant Inverse proportion – relationship in which the product of two variables is constant