Units and data EQ: What is the correct format for numbers in scientific notation? How are numbers converted using the metric system? How are significant figures counted?

Standard Notation to Scientific Notation Positive exponent: Number ≥ 1 Negative exponent: Number ≤ 1 Exponent = Number of times the decimal is moved Only 1 non-zero number in front of decimal Ex: 1, 234.98 0.003251

Scientific Notation to Standard Notation Positive exponent: move decimal to the right Negative exponent: move decimal to the left Ex: 3.65 x 104 2.12 x 10-3

Practice

SI base Units Quantity Base Unit Time Seconds (s) Length Meter (m) Mass Kilogram (kg) Temperature Kelvin (K) Amount of a substance Mole (mol) Electric current Ampere (A) Luminous Intensity Candela (cd) Note: ˚C + 273.15 = Kelvin (K) or Kelvin (K) – 273.15 = ˚C

Metric Conversions Gee Man…kingwood High does [math, Language, grammer] during class monday…maybe naps! Giga Mega…kilo Hecta deca [meter, Liter, gram] deci centi milli…micro nano! 109 106 …103102101 Units 10-110-210-3…10-610-9

Practice 35 mm = ____ cm 17649.3 cm = ____Mm 14,443 L = ____ kL 1.9 mL = _____nL 0.00056 kg = ____ g 16 mm = ____ km 35.4 L = ____ dL 0.01096 kL = ____ mL

Dimensional Analysis All other unit conversions can be made through dimensional analysis, which uses conversion factor to switch between units. Conversion factors are simply the equivalence of one unit to another. Ex. 1 min = 60 sec or 1 meter = 3.28 feet 1st: Put the number in the problem over 1 2nd: Determine a conversion factor 3rd: Apply conversion factor so units are the same diagonally (reading from left to right)

Practice: 18.77 g to mg 37.4 cm to m 4.7 days to sec 956,765 hours to weeks

Sig Figs measure the degree of precision of a Significant Figures Sig Figs measure the degree of precision of a measurement.

Rules for counting sig figs: There are ONLY two rules to remember when counting the # of Sig Figs.

Rule #1: Don’t start counting till you get to a number that isn’t a zero. Rule #2: Once you start counting, don’t stop till you’ve counted all the digits, including zeroes.

And you need to remember a little geography: Where is the Atlantic Ocean, and where is the Pacific Ocean? Decimal is Present: Start counting from the first non-zero number from the Pacific (left) side. Decimal is Absent: Start counting from the first non-zero number from the Atlantic (right) side.

Examples 2.55 3 S.F. 0.2500 4 S.F. 5 S.F. 100.25

Examples 135 3 S.F. 100 1 S.F. 3 S.F. 10500

Examples 350 0.0020 17,500 27.02 2060 135.0

Rounding Starting from the left find the 1st nonzero number….this is the MOST significant digit, then round accordingly Numbers BEFORE decimal = convert to zero Numbers AFTER decimal = Drop EXAMPLE: round to 2 sig figs 120,320 0.00265 7532.0156 Now round each to 3 sig figs

Using sig figs in calculations

For multiplication and division:

Your answer should have the fewest number of significant figures from the problem

233.65 x 200 = 46730 5 S.F. 1 S.F. 4 S.F.? Answer must be recorded as 50,000 cm2 It can have only one sig fig.

What is the correct answer? 610 x 6.20 = 3782 2 S.F. 3 S.F. 3800 What is the correct answer?

Example: You calculate the density of an object with mass of 24 Example: You calculate the density of an object with mass of 24.300 grams, and volume of 62.5 ml. How many sig figs in your answer? Density=mass/volume 24.300/62.5 = 0.3888 Correct Sig. Figs. = 0.389

For addition and subtraction

Your answer can not contain more decimal places than the least precise measurement.

Line up the decimal points in the numbers. 2.515 + 1.3 +12.00 =????

2.515 1.3 + 12.00 15.815 Answer stops here

Calculations & Sig Figs Recap Multiplication & Division Fewest Number of Significant figures Addition & Subtraction Fewest Numbers after the decimal (least precise)

Sig Figs & Scientific notation

The number of sig figs comes from the number written before the times sign.

Examples 3.50 x 1023 3 S.F. 5.0 x 10 -4 2 S.F. 1 S.F. 3 x 10-4

Density Physical property of matter Measure of mass per unit volume g/L or g/cm3 1 mL = 1 cm3 Ex. What is the density of a metal that is 37.2 cm3 and weighs 260.8 g? How many numbers should your answer have? Why?

Application: % Error % Error = experimental – theoretical x 100 Example: As the result of experimental work, a student finds the density of a liquid to be 0.1369 g/cm3. The known density of that liquid is 0.1478 g/cm3. What is the percent error of this student’s work? Practice: The melting point of potassium thiocyanate determined by a student in the laboratory turned out to be 174.5 oC. The accepted value of this melting point is 173.2 oC. What is the percent error in this reading?