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Measurements Scientific Notation Significant Figures

SI System 1795 French scientists adopt system of standard units called the metric system. In 1960 the metric system was revised to the SI system. Systeme Internationale d’Unites Base Units Time – second Length – meter Mass - kilogram

Base Units Defined unit in a system of measurement that is based on an object or event in the physical world. Independent of other units.

Base Units Quantity Base Unit Time Second (s) Length Meter (m) Mass
Kilogram (kg) Temperature Kelvin (K) Amount of a Substance Mole (mol) Electric Current Ampere (A) Luminous Intensity Candela (cd)

Derived Units Unit that is defined by a combination of base units.
Volume – the space occupied by an object. derived unit – m3 cm3 = mL Density – ratio that compares mass of an object to its volume.

Density How can we rearrange this equation if we have the density and volume.

Temperature Kelvin scale, founded by William Thompson who was known as Lord Kelvin. Water freezes at 273 K It boils at 373K The scale is the same as Celsius, just different temperature points Celsius = Kelvin Kelvin – 273 = Celsius

Problems If the density of an object is 2.70 g/cm3 and the mass of the object is 1.65g, what is the volume of the sample? Density Triangle

Problem Convert the following: 357oC to Kelvin -39oC to Kelvin
357oC = 630K -39oC to Kelvin -39oC = 234K 266K to Celsius 266K – 273 = -7oC 332K to Celsius 332K – 273 = 59oC

Graphs A visual display of data. Circle Graphs or Pie Charts
Show parts of a fixed whole Usually broken into % Bar Graphs Show how quantities vary Measured quantity on y-axis Independent variable on x-axis

Graphs Line Graphs Most common in chemistry
Independent variable on x-axis Dependent variable on y-axis Can determine slope of line

Prefixes SI Prefixes mega (M) 106 kilo (k) 103 basic unit
deci (d) 10-1 centi (c) 10-2 milli (m) 10-3 micro (µ) 10-6 nano (n) 10-9 pico (p)

Scientific Notation Expresses numbers as a multiple of two factors:
A number between 1 and 10. Ten raised to a power or exponent. Exponent tells you how many times the first factor must be multiplied by 10. A number larger than 1 expressed in scientific notation, the power of 10 is positive. A number smaller than 1 has a negative power of 10.

Problems Express the following in scientific notation
Put the following scientific notation numbers in standard notation.

Multiplying and Dividing with Scientific Notation
When multiplying terms in scientific notation, you multiply the coefficients, keep your base of 10 and add the exponents. When dividing terms in scientific notation, you divide the coefficients, keep your base of 10 and subtract the exponents.

Multiplying and Dividing

Addition and Subtraction with Scientific Notation
When adding or subtracting in scientific notation: Get terms to have the same exponent. Add or subtract the coefficients. Keep your base of ten. Keep the exponent that both terms contained.

Adding and Subtracting

Significant Figures Indicate the uncertainty of a measurement.
Include all known digits plus one estimated digit. If the earth is 4 billion years old, will it be 4 billion and one next year? If I ask you how tall you are and you say between 5-6 feet, that isn’t very interesting. You left out the interesting information. Read the bottom of the meniscus (line AB) ml

Rules for Significant Figures (Digits)
All non-zero digits are significant. 127.34 Contains 5 significant digits. All zeros between two non-zero digits are significant. Contains 6 significant digits. Unless specifically indicated by the context to be significant, ALL zeros to the left of an understood decimal point, but to the left of a non-zero digit are NOT significant. 109,000 Contains 3 significant digits

Rules continued… All zeros to the left of an expressed decimal point and to the right of a non-zero digit ARE significant. 109,000. Contains 6 significant figures. All zeros to the right of a decimal point, but to the left of a non-zero digit are NOT significant. Contains 3 significant figures. The single zero conventionally placed to the left of the decimal point is NEVER significant

Rules continued… ALL zeros to the right of the decimal point and to the right of a nonzero digit ARE significant. 30.00 Both contain 4 significant digits. Counting numbers and defined constants have an infinite number of significant digits. 60 s = 1 min 11 soccer players

Operations with Significant Figures
Multiplication and Division The answer contains the same number of significant figures as the measurement with the least amount of significant figures. Addition and Subtraction The answer has the same number of decimal places as the measurement with the least amount of decimal places.

Precision vs. Accuracy Precision Accuracy
The agreement between measurements. How close a set of measurements are to each other. Accuracy The nearness of a measurement to its actual value. How close you are to the true value.

Precision vs. Accuracy

These thermometers have different levels of precision
These thermometers have different levels of precision. The increments on the left are 0.2, but the ones on the right are How should their temperatures be recorded? 37.53 5.8

Percent Error The ratio of an error to an accepted value.

Example You analyze a sample of copper sulfate and find that it is 68% copper. The theoretical value of copper is 80%. What is the percent error?

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