Chapter 2 Data Analysis p24-51

What is the Mass of the Sun? 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this in a simpler way??

Purpose of Scientific Notation Scientific notation was developed to solve the problem of writing very large and small numbers. Numbers written in scientific notation have two parts: a stem, which is a number between 1 & 10, and a power of 10. 93,000,000 = 9.3 x 107 Stem Power of 10

Purpose of Scientific Notation Let’s take a closer look at the parts of a number written in scientific notation to see how it works. 93,000,000 = 9.3 x 107 Stem The stem is always a number between 1 and 10. In this example, 9.3 is the stem and it is between 1 and 10.

Purpose of Scientific Notation The power of ten has two parts. There is a base and there is an exponent Exponent = 7 93,000,000 = 9.3 x 107 Base = 10 The base will always be 10. The exponent in this example is 7.

Convert Standard Form to Scientific Notation Write 8,760,000,000 in scientific notation. Step 1: Move the decimal until you have a number between 1 and 10 then drop the extra zeros. . 8 7 6 0 0 0 0 0 0 0 . 8.76 is the Stem

Convert Standard Form to Scientific Notation Write 8,760,000,000 in scientific notation. Step 2: The number of places you moved the decimal will be the exponent on the power of 10 . . 8 7 6 0 0 0 0 0 0 0 9 places 8.76 is the Stem 10 9 is the Power of 10

Convert Standard Form to Scientific Notation Write 8,760,000,000 in scientific notation. Step 3: Write the number so it is the stem times the power of ten. . . 8 7 6 0 0 0 0 0 0 0 9 places 8.76 is the Stem 10 9 is the Power of 10 8.76 x 10 9 = 8,760,000,000

Convert Standard Form to Scientific Notation Write the following numbers in scientific notation. 660,000,000 = 90300 = 397 = 6.6 x 108 9.03 x 104 3.97 x 102

Convert Standard Form to Scientific Notation Write 0.00000000482 in scientific notation. Step 1: Move the decimal until you have a number between 1 and 10 then drop the extra zeros. 0 0 0 0 0 0 0 0 0 4 8 2 . . 4.82 is the Stem

Convert Standard Form to Scientific Notation Write 0.00000000482 in scientific notation. Step 2: The number of places you moved the decimal will be the exponent on the power of 10. The exponent will be negative because you started with a number less than 1. 0 0 0 0 0 0 0 0 0 4 8 2 . . 9 places 4.82 is the Stem 10 -9 is the Power of 10

Convert Standard Form to Scientific Notation Write 0.00000000482 in scientific notation. Step 3: Write the number so it is the stem times the power of ten. . . 0 0 0 0 0 0 0 0 0 4 8 2 9 places 4.82 is the Stem 10 -9 is the Power of 10 4.82 x 10 -9 = 0.00000000482

Convert Standard Form to Scientific Notation Write the following numbers in scientific notation. 0.00543 = 0.00000074 = 0.03397 = 5.43 x 10 -3 7.4 x 10 -7 3.397 x 10 -2

Convert Scientific Notation to Standard Form Write 1.98 x 109 in standard form. The exponent tells us to move the decimal 9 places. A positive exponent means the number is bigger than the stem. To make 1.98 bigger, we must move the decimal to the right. 1 9 8 x 10 9 . . 0 0 0 0 0 0 0 9 places 1.98 x 109 = 1,980,000,000

Convert Scientific Notation to Standard Form Write the following numbers in standard form. 2.9 x 104 = 6.87 x 106 = 1.008 x 109 = 29,000 6,870,000 1,008,000,000

Convert Scientific Notation to Standard Form Write 5.37 x 10-9 in standard form. The exponent tells us to move the decimal 9 places. A negative exponent means the number is smaller than the stem. To make 5.37 smaller, we must move the decimal to the left. 0 0 0 0 0 0 0 0 0 . 5 3 7 x 10 -9 . 9 places 5.37 x 10-9 = 0.00000000537

Convert Scientific Notation to Standard Form Write the following numbers in standard form. 2.9 x 10-4 = 6.87 x 10-6 = 1.008 x 10-9 = 0.000 29 0.000 006 87 0.000 000 001 008

Why are measurement standards important? What is a standard? It is an exact quantity that people agree to use for comparison. Why are measurement standards important? A meter in the U.S. is the same as a meter in France.

Units for Measurement Used in Science Length Metric ruler: Measured in meters (m) Volume Graduated cylinder: Measured in liters (L) Mass Balance: Measured in grams (g) Temperature Thermometer: Measured in degrees Celsius (OC)

International Standard Prefixes (SI) MUST KNOW: Kilo = 1,000 or 103 Centi = .01 or 10-2 Milli = .001 or 10-3

Conversions WITHIN the Metric System You can simply move the decimal point… But you have to know how to move it.

METRIC UNIT CONVERSIONS Move decimal 1 place to the right for each step. BASE Move decimal 1 place to the left for each step.

METRIC UNIT CONVERSIONS Use this to remember the metric prefixes: “King Henry Died Drinking Chocolate Milk” The first letters represent the prefixes (kilo, hecto, deka, deci, centi, milli)

EXAMPLE It is common for runners to do a “10K” run. This means they are running 10 kilometers. How many millimeters is that??? A lot!!!!!

Answer Look at the staircase graphic… Start on the prefix “kilo” Move down the staircase 6 steps (don’t count the step you start on) to get to the prefix “milli” This means you move the decimal point 6 places to the RIGHT 10 Kilometers is converted to 10,000,000 mm

Making Metric Conversions Home Make the following metric conversions. 1,000 grams = kg 500 mg = g 2.25 liters = ml 0.07 g = kg 1 kilometer = m 650 cm = m 0.30 kg = mg 1 0.5 2250 0.00007 1000 6.5 300,000 Table

Making Metric Measurements - Length Choose the most appropriate measure. Length of a football field 1 km, 100 m, 1,000 um, 10 cm, 100 mm Length of a newborn baby 0.5 m, 0.05 km, 500 um, 5,000mm, 50 cm Thickness of a sheet of paper 0.1 mm, 0.1 cm, 0.01 m, 1 km, 10 um

Making Metric Measurements - Mass The following are approximations to help you get a feel for metric units of mass. We will deal only with the most common units. 1 kilogram  Just over 2 pounds 1 gram  Mass of a raisin 1 milligram  Mass of a grain of sand

Making Metric Measurements - Mass Choose the most appropriate measure. Mass of a nickel 50 g, 5 mg, 0.5 kg, 5 g, 500 mg Mass of an aspirin 500 mg, 0.5 mg, 500 g, 50 kg, 50 g Mass of an average adult 700 kg, 0.7 g, 700 mg, 7,000 g, 70 kg Mass of a baseball 400 mg, 0.4 g, 4 kg, 400 g, 40 g

Making Metric Measurements - Volume The following are approximations to help you get a feel for metric units of volume. We will deal only with the most common units. 1 liter  Just over 1 quart 1 milliliter  About 20 drops

Making Metric Measurements - Volume Choose the most appropriate measure. Volume of a car’s gas tank 50 l, 5 l, 500 ml, 50 ml, 500 l Volume of a teaspoon 0.5 l, 0.5 ml, 5 l, 5 ml, 500 ml Volume of a can of soda 500 l, 0.05 l, 500 ml, 0.5 ml, 0.005 ml Volume of a syringe 0.02 ml, 200 ml, 0.02 l, 2 l, 2 ml

Putting It All Together prefix symbol unit centi- c m meter (0.01) hundredth of a meter milli- L m liter (.001) thousandth of a liter kilo- k g gram (1000) thousand grams

VII. The Temperature Scales Kelvin Scale (K) SI Absolute temperature. Same units as Celsius but the freezing point of water is 273K, and the boiling point is 373K. Celsius Scale ( ˚C) SI common temperature the freezing point of water is 0O C and the boiling point is 100O C. Fahrenheit Scale (˚F) Used only in the U.S. Water freezing point 32˚F, and boiling point 212˚F.

Converting from Kelvin to Celsius TC = TK – 273 ex. ? C = 52K ____˚C = 52K – 273 TK = TC + 273 ex.?K = 70˚C _____K = 70˚C + 273

Converting from Celsius to Fahrenheit TF = 1.80(TC) + 32 Ex. 41˚C = ? ˚F TF = 1.80 (41˚C) + 32 TF = __________ ˚F

Making Metric Measurements Home Name at least three benefits of the Metric System. There is a consistent relationship between units - Prefixes stay the same, It’s easy to convert. The whole world uses it. The base units are used to “derive” all other units in the System International (SI)

Derived units are defined by a combination of base units. Density = g/cm3

VII. Density can be defined as the amount of matter present in a given volume of substance. Density = mass/ volume

Practice Mercury has a density of 13.6g/mL. What volume of mercury must be taken to obtain 225g of the metal?

IV. Accuracy and Precision Compare and contrast accuracy /precision. Accuracy- refers to how close a measured value is to an accepted value. Precision – Refers to how close a series of measurements are to one another.

Accuracy vs Precision Is the soda filling machine below accurate and/or precise? This machine is precise. It delivers the same amount of soda each time. This machine is not accurate. It is not putting 12 oz in each can.

Accuracy vs Precision Is the soda filling machine below accurate and/or precise? This machine is precise. It delivers the same amount of soda each time. This machine is accurate. It is putting 12 oz in each can.

Accuracy and Precision cont… The difference between an accepted value and an experimental value is the error. The ratio of an error to the correct value, is percent error.

Formula for Percent Error = Value accepted – Value experimental x 100% Value accepted

Dimensional Analysis A technique for converting from one unit to another

Beyond the metric System If you need to convert to or from units that are NOT metric units, we use a unit conversion technique called “dimensional analysis”

Conversion Factors In dimensional analysis, we make conversion factors into fractions that we will multiply by. For example, one conversion factor is: 1 inch=2.54 cm We can make (2) fractions out of this… 1 inch OR 2.54 cm 2.54 cm 1 inch

Which number goes on top and bottom in the conversion factor? Usually… The unit you WANT goes on TOP The unit you want to CANCEL goes on BOTTOM

Dimensional Analysis EXAMPLE A PENCIL IS 17.8 CM LONG, WHAT IS ITS LENGTH IN INCHES? Start with the “given” 17.8 cm

Dimensional Analysis A PENCIL IS 17.8 CM LONG, WHAT IS ITS LENGTH IN INCHES? Multiply by the “conversion factor” 17.8 cm x 1 inch = 2.54 cm

Dimensional Analysis A PENCIL IS 17.8 CM LONG, WHAT IS ITS LENGTH IN INCHES? Cross cancel “like” units 17.8 cm x 1 inch 2.54 cm

Dimensional Analysis A PENCIL IS 17.8 CM LONG, WHAT IS ITS LENGTH IN INCHES? Do the math using the correct number of significant figures (based on given information) 17.8 cm x 1 inch = 7.01 inches 2.54 cm

Dimensional Analysis Example A pencil is 8.1 inches, how many cm is it? 8.1 inches x 2.54 cm = 21 cm 1 inch The unit we WANT is cm so we put 2.54 cm on TOP of the conversion factor

Multi-Step Example Sometimes, we must “string” several conversion factors together to get from one unit to another. Ex.- Mr. Gray’s class is 55 minutes long. How many days long is this??!!

Multi-Step Example Need to go from min hrs days 55 min x 1 hr x 1 day = 0.038 days 60 min 24 hrs Note how “like” units can be cross-canceled (canceled out)

Practice Perform each of the following conversions, being sure to set up clearly the appropriate conversion factor in each case. 55min to hours 6.25km to miles Apples cost $0.79 per pound. How much does 5.3 lb of apples cost?

Significant Figures Significant figures include the number of all known digits reported in measurement plus one estimated digit. Non-zero numbers are always significant Zeros between non-zero #s are always significant All final zeros to the right of the decimal place are significant

Significant rules cont. 4. Zeros that act as placeholders to the left of the decimal are not significant. Positive exponents in scientific notation are not significant. 5. Zeros that are to the right of the decimal are always significant. Negative exponents! 6. Counting numbers and defined constants have an infinite number of significant figures.