Measurement Scientific Notation and the Metric System

Theory vs. Law A theory is an accepted explanation of an observed phenomenon until repeated data and observation conflict with the theory A theory is a detailed explanation that helps scientists understand a phenomenon A law is a statement or mathematical equation that describes a basic fact or relationship found in the universe

Reliability in Measurement Precision same results again and again under the same conditions Accuracy Close to the accepted value Accepted Value = the correct answer

4 Accuracy vs. Precision

The Metric System The United States uses the States Customary system (USCS), but most other countries use the International System of Units or the metric system. The metric system uses a decimal system where all units are related by a factor of 10.

International System of Unit (SI Base Units) MassLengthTime Count, quantity Temperature Kilogram(kg) Meter (m) Second(s) Mole(mol) Kelvin(K)

Derived SI Units AreaVolumeForcePressureEnergy m2m2m2m2 m3m3m3m3NewtonPascalJoule

Metric Prefixes KiloHectoDeka Base Unit (m, g, L, sec, etc) decicentiMilli k10 3 h10 2 da d10 -1 c10 -2 m10 -3

Measurement to Scale

10 Density How heavy something is for its size. The ratio of mass to volume for a substance. D = M/V

Scientific Notation A number written as the product of two numbers. A coefficient (number between 1-9) A coefficient (number between 1-9) 10 raised to a power 10 raised to a power Useful for large numbers. For example 1g of hydrogen contains 602,000,000,000,000,000,000,000 atoms. For example 1g of hydrogen contains 602,000,000,000,000,000,000,000 atoms. That is 6.02 x atoms. That is 6.02 x atoms.

Converting to Scientific Notation Moving the decimal to the left gives a positive exponent. Example: 36,000= Example: 36,000= 3.6 x x 10 4 Moving the decimal to the right gives a negative exponent. Example: = Example: = 8.1 x 10 -3

Try these on your own: = 3.2 x 10 5 = 1.72 x = 1.37 x ,

Rules for Multiplication Multiply the coefficients and add the exponents. Example 1: (3.0 x 10 4 ) x (2.0 x 10 2 ) = Example 1: (3.0 x 10 4 ) x (2.0 x 10 2 ) = 6.0 x 10 6 Example 2: (4.0 x ) x (1.0 x 10 2 )= Example 2: (4.0 x ) x (1.0 x 10 2 )= 4.0 x 10 -5

Rules for Division Divide the coefficients and subtract the exponents. Example 1: (3.0 x 10 4 ) / (2.0 x 10 2 ) = Example 1: (3.0 x 10 4 ) / (2.0 x 10 2 ) = 1.5 x 10 2 Example 2: (8.0 x ) / (4.0 x 10 4 ) = Example 2: (8.0 x ) / (4.0 x 10 4 ) = 2.0 x 10 -7

Rules for Addition and Subtraction Before you add or subtract in scientific notation, the exponents must be the same. Example 1: 5.40 x x 10 2 = Example 1: 5.40 x x 10 2 = 54.0 x x 10 2 = 54.0 x x 10 2 = 60.0 x 10 2 = 6.0 x x 10 2 = 6.0 x 10 3 Example 2:8.5 x – 3.0 x = Example 2:8.5 x – 3.0 x = 85 x x = 85 x x = 82 x = 8.2 x x = 8.2 x 10 -2