Matter Part 2

Scientific Notation

What is Scientific Notation? A way to express either very large or very small numbers

Scientific Notation Each number represented in scientific notation has 3 parts: The coefficient must be greater than 1 or less than 10 The exponent can be positive or negative Write down the 3 parts

Scientific Notation Circle the numbers that are in scientific notation. 14.5x108 3.9x10-4 1.6984275x1014 0.682x10-1 1.90x100 Ask about the zero

Scientific Notation

Converting from Standard form to Scientific Notation Standard Form Scientific Notation 0.0047 (original number is less than 1) _____________ 22,598.7 (original number is greater than 10) ______________ 595 _______________ 4.7 x 10-3 2.25987 x 104 5.95 x 102

Converting from Scientific Notation to Standard Form A positive exponent means the number is very big Move the decimal to the right A negative exponent means the number is very small Move the decimal to the left

Converting from Scientific Notation to Standard Form Draw in the loops to indicate how many zeros you need to add

Converting from Scientific Notation to Standard Form Scientific Notation Standard Form 3.772x104 (exponent is positive) _____________ 9.8x10-3 (exponent is negative) _____________ 5.36042x106 ______________ 37,720 .0098 5,360,420

Performing Calculations in Scientific Notation ***use the “ee” button on your calculator Example: (3.4x106)(8.792x109) = In your calculator, enter “3.4 2nd ee 6 X 8.792 2nd ee 9 enter” (3.4x106)(8.792x109) = 2.99x1016

Practice Calculations (5.44x10-3)(6.669x108) = (1.72x1016)(3.99x10-5) = (8.116x103)

Precision vs. Accuracy Precision – the closeness of a set of measurements of the same quantity made in the same way Accuracy – the closeness of measurements to the correct or accepted value of the quantity measured

Percent Error If I estimate the weight of my cat to be 10 pounds but her actual weight is 13.75 pounds, what is my percent error?

Significant Figures

Sig Figs What are sig figs? The number of figures that are shown with some degree of reliability The number of digits used to express a measured or calculated value Why do we use sig figs? To show how accurate a number is

Rules for Significant Figures Nonzero numbers are ALWAYS significant. 1287 g 78,483 cm 58 mL 638 mol = 4 Sig Figs = 5 Sig Figs = 2 Sig Figs = 3 Sig Figs

Rules for Significant Figures Zeros in-between nonzero numbers are ALL significant. 101 mol 20,375 cd 1001 J 908 s = 3 Sig Figs = 5 Sig Figs = 4 Sig Figs = 3 Sig Figs

Rules for Significant Figures Zeros after nonzero numbers (trailing zeros) WITH A DECIMAL PRESENT are significant 6.0 mg 678.10 Kg 80.0 m 12.00 mL = 2 Sig Figs = 5 Sig Figs = 3 Sig Figs = 4 Sig Figs

Rules for Significant Figures Zeros in front of nonzero digits (preceding zeros) are not significant. They are called place holders. 0.78 Kg 0.0309 cd 290 amp 300 s = 2 Sig Figs = 3 Sig Figs = 2 Sig Figs = 1 Sig Figs

Rules for Significant Figures Counting numbers and defined constants have an infinite number of significant figures. 1 dozen = 12 78 pencils 32 books 1 pair = 2 = Infinite Number of Sig Figs = Infinite Number of Sig Figs = Infinite Number of Sig Figs = Infinite Number of Sig Figs

Zeros that are significant. 202 cm 510002 L 144.0 kg 670.00 cd = 3 Sig Figs = 6 Sig Figs = 4 Sig Figs = 5 Sig Figs

Zeros that are NOT significant, PLACE HOLDERS. = 1 Sig Figs 50 g 0.0072 m 0.0321 J 9000 L = 2 Sig Figs = 3 Sig Figs = 1 Sig Figs

= 4 Sig Figs = 3 Sig Figs = 4 Sig Figs = 4 Sig Figs 80020 s 0.00401 kg Zeros that are significant (called Trailing) and zeros that are not significant (call Place Holder). = 4 Sig Figs 80020 s 0.00401 kg 0.03020 Amp 10230 L = 3 Sig Figs = 4 Sig Figs = 4 Sig Figs

Making Calculations with Significant Digits Multiplying and Dividing The final answer is rounded to have the same number of significant figures as the measurement with the least number of significant figures. 755 cm x 33 cm = 24915 92 m x 20 m = 1840 25000 cm2 2000 m2

0.894 g / 2.0 g = 0.447 g 40.0 x 3.8 = 152 203 x 4589 = 931567 10259 / 789 = 13.00253485 96.0 / 75.0 = 1.25 101 x 0.020 = 2.02 0.45g 1.50 932000 13.0 1.25 2.0

Making Calculations with Significant Digits Adding and Subtracting The final answer is rounded so that it has the same number of digits past the decimal as the measurement with the least number of digits past the decimal 120.60 89.001 6.3 215.901 + 215.9

756.05 23.02 733.03 − 733.03 9.002 2.32 45.659 56.981 + 56.98

45 32.5 12.5 − 13

Metric System/ SI units A universal system of measurement Base units: Mass: measured in grams (g) Volume: measured in liters (L) Length: measured in meters (m)

Metric Conversions Metric Prefixes Kilo (k) 1000 103 Hecto (h) 100 102 Prefix & Symbol Numeric Multiplier Exponent Kilo (k) 1000 103 Hecto (h) 100 102 Deca (da) 10 101 Base/ No Prefix (m, L, g) 1 Deci (d) .1 10-1 Centi (c) .01 10-2 Milli (m) .001 10-3

Metric Conversions King Henry Died by Drinking Chocolate Milk How many kilometers are in 14,220 meters? How many millimeters are in are in 562 decimeters?

Metric Conversions Practice _____________________________________________ 5.6kg = ______ g 15.7daL = _____cL 75mL = ______L 15,000dm = _____km 16cm = _____mm 0.06g = _____cg

Dimensional Analysis Convert 3.7 feet to inches. Dimensional analysis steps: 1. Set up a picket fence. 2. Start with what you’re given in the problem. 3.7 ft

Dimensional Analysis Place what you’re looking for off to the side. inches? Choose a conversion factor. 12 inches = 1 foot Place your conversion factor in your picket fence so your units cancel. 3.7 ft 12 inches inches? 1 ft Solve and include the correct unit on your answer. 3.7 x 12 = 44.4 inches

Dimensional Analysis Practice: Convert 50 years into seconds. How many cups are in 50mL? (1L = 4.226cups) Convert 3.8km/s to mi/week. (1600m = 1mi) A particular brand of gasoline has a density of 0.737g/ml. How many grams of this gasoline would fill a 12.9 gallon tank? (1gallon = 3.79 liters) Alan is going to the Boy Scouts Jamboree in D.C. next summer and he has been asked to bring the smores supply for all the boys going from the district in Oregon. Each giant chocolate bar makes 16 smores. Each boy will be limited to exactly 3 smores. The problem is that he has to buy the chocolate once he gets to D.C. because there will be too many of them and they may melt in the summer heat. On average, the stores only carry 25 of these giant chocolate bars in stock. How many stores will he have to visit if there are 2,225 boys?

Density Density is a measure of how much “stuff” is contained in a certain volume of a substance. A low density item is “light” in comparison to something else of the same volume Which is more dense? A or B? Answer: A – there is more “Stuff” for the same volume! A B

Density Equation D = m/V D = density Units for density = g/cm3 or g/ml M = mass Unit for mass = grams (g) V = volume Units for volume = cm3 (if it is a solid) or mL (if it is a liquid)

Example Problem #1 You are given a cube made out of an unknown substance and want to find out the density. How would you find the volume of a cube? First you can measure one side – let’s say it is 2cm. Volume = l x w x h 2 x 2 x 2 = 8 cm3 Then you can weigh it on a scale – let’s say its mass is 240 g D = m/V D = 240g/8cm3 D = 30 g/cm3

Example Problem #2 You are given an irregularly shaped solid made of an unknown substance and are asked to find its density. How would you find the volume? To find the volume you can drop it in a cylinder of water and note the change in volume – let’s say the water level rises from 22mL to 32mL. The volume of the solid would be 10mL Then you can weigh it on a scale – let’s say the mass is 100g D = m/V D = 100g/10mL D = 10 g/mL

Float or Sink? Density determines whether an object will float or sink. If an object is less dense than the fluid it is immersed in, it will float If it is more dense, it will sink

An 800 ml quantity of vanilla ice cream has a mass of 600 g An 800 ml quantity of vanilla ice cream has a mass of 600 g. The manufacturer then bubbles air into the ice cream so that its volume increases by 400 ml. What is the ice cream’s approximate density? 0.5 g/ml 2.0 g/ml 0.75 g/ml 1.5 g/ml

What is the mass of a 500 ml sample of seawater with a density of 1 What is the mass of a 500 ml sample of seawater with a density of 1.025 g/ml? 487.8 g 0.002 g 512.5 g 529.2

A block of maple wood with a volume of 405 cubic centimeters and a density of 0.67 grams/cubic centimeter is sawed in half. What is the density of the two smaller blocks? 0.335 grams/cubic centimeters 271.4 g 604.5 g/cubic centimeters 0.67 g/cubic centimeters

A sample of an element has a mass of 132. 6g and a density of 2 A sample of an element has a mass of 132.6g and a density of 2.55 g/ml. What is the volume in liters of the sample? .338.1 L 52 L 0.02 L 0.052 L