Chapter 5 1

Objective The student will be able to: express numbers in scientific and decimal notation. SOL: A.10, A.11 Designed by Dr. Shah, Blue Valley High School 2

How wide is our universe? 210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation. 3

Scientific Notation A number is expressed in scientific notation when it is in the form a x 10 n where a is between 1 and 10 and n is an integer 4

Write the width of the universe in scientific notation. 210,000,000,000,000,000,000,000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make this number be between 1 and 10? Between the 2 and the 1 5

2. 10,000,000,000,000,000,000,000. How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x

1) Express in scientific notation. Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative x

Write in scientific notation x x x x

2) Express 1.8 x in decimal notation ) Express 4.58 x 10 6 in decimal notation. 4,580,000 On the graphing calculator, scientific notation is done with the button x 10 6 is typed

4) Use a calculator to evaluate: 4.5 x x Type You must include parentheses if you don’t use those buttons!! (4.5 x 10 -5) (1.6 x 10 -2) Write in scientific notation x

5) Use a calculator to evaluate: 7.2 x x 10 2 On the calculator, the answer is: 6.E -11 The answer in scientific notation is 6 x The answer in decimal notation is

6) Use a calculator to evaluate (0.0042)(330,000). On the calculator, the answer is The answer in decimal notation is 1386 The answer in scientific notation is x

7) Use a calculator to evaluate (3,600,000,000)(23). On the calculator, the answer is: 8.28 E +10 The answer in scientific notation is 8.28 x The answer in decimal notation is 82,800,000,000 13

Write (2.8 x 10 3 )(5.1 x ) in scientific notation x x x x

Write in PROPER scientific notation. (Notice the number is not between 1 and 10) 8) x x ) x 10 4 on calculator: x

Scientific notation We use scientific notation to describe very large and very small numbers The format for scientific notation is X x 10 y X is a number between 1-10 Y is a negative number if number is smaller than 1 and positive if number is larger than 1. Y signifies how many places we will move the decimal 16

Write x 10 5 in scientific notation x x x x x x x

Scientific notation We use scientific notation to describe very large and very small numbers The format for scientific notation is X x 10 y X is a number between 1-10 Y is a negative number if number is smaller than 1 and positive if number is larger than 1. Y signifies how many places we will move the decimal 18

Units Units – part of the measurement that tells us what scale or standard is being used to represent the results of the measurement Different units of measure –English System –Metric system –International system (SI) [based on metric] 19

More units SI units – you will be required to know these!!!! –Mass = kg (kilogram) –Length = m (meter) –Time = s (second) –Temp = K (kelvin) 20

Prefixes and metric system You are expected to Memorize the information from the table above 1 Megameter = 1 x 10 6 meters 1 kilometer = 1 x 10 3 meters 21

How to use prefixes milli- means or Put a 1 in front of the unit. Put an equal sign after the unit. rewrite the unit So, millimeter becomes: 1 millimeter = millimeter Lastly, on the unit to the right of the equal sign remove the prefix and substitute with value that prefix represents. 22

How to use prefixes 1 millimeter= millimeter remove the prefix on the unit to the right of the equal sign thus: 1 millimeter = ________meter Now substitute the value of the prefix in: 1 millimeter = __0.001__meters or 1 millimeter = ____10 -3 __meters 23

expectations I expect you to memorize or know the following equality: –1 in. = 2.54 cm Length = measure of distance Volume = measure of 3-d space Mass = quantity of matter 24

Uncertainty in measurement When taking a measurement, there is always certain digits and estimated digits. The last digit of ALL measurements are estimated. This block is between 3 and 4 cm. I could record it as 3.6 cm. Here the 6 would be estimated

Significant figures The concept of significant figures helps us in calculations with estimations. First we must learn the rules for S.F. –1. non-zero #s are always significant –2. zeros 1. leading zeros are NEVER significant ( = 2 S.F.) 2. captive zeros are ALWAYS significant ( = 4 SF) 3. Trailing zeros are significant if there is a decimal ( = 7 SF) –3. Exact numbers are counted as infinite SF 3 eggs = infinite SF 26

Sig Fig trick Draw US. Atlantic ocean = decimal absent Pacific ocean = decimal present 27

Arithmetic with S.F. Addition/subtraction: least # places after the decimal Multiplication/division: least # of s.f. Rounding 28

s.f. add/subtract Rule: use the least number of places Example: = (in calculator)= 16.6 (Final answer in correct # of s.f.) Example = 39.3 (in calculator) = 39 (Final answer in correct # of s.f.) 29

s.f. mult/div Rule= use least # of s.f. for answer Example: x 63.7 x 6040 = (in calculator) = (final answer in correct s.f.) Example: 30 / 2.0 = 15 (in calculator) = 20 (final answer in correct # of s.f.) 30

Chapter 5 (cont.) Problem solving and dimensional analysis 31

objective and definitions objective: Learn how dimensional analysis can be used to solve various problems conversion factor: ratio that relates 2 units ex cm/ 1 in. equivalence statement: numerical relationship between 2 units ex cm = 1 inch There are 2 conversion factors for each equivalence statement 1 in./2.54 cm and 2.54 cm/ 1 in. dimensional analysis – using conversion factors to change from 1 unit to another units – part of measurement tells us which scale/standard is being used 32

Converting from one unit to another To carry out dimensional analysis, you must multiply by the conversion factor that puts the units you want to cancel on bottom and units you desire on top. Example: An Italian bicycle has its frame size given in 62 cm. What is the frame size in inches? Start the problem with what is given. 33

Example problem 62 cm x 1in. = 24 inches 2.54 cm Be sure to include proper # of sig figs in answer. 34

Multistep Dimensional Analysis Most problems will require multiple conversion factors. Ex. The length of a marathon is 26.2 miles How many km is that? 1 mile = 1760 yards 1 meter = yards 35

multistep problem (cont.) 26.2 miles x 1760 yards 1 mile x 1 meter yd x 1 km 1000 m = On calculator you type 26.2 x 1760 / / 1000 = You should get km 36

Dimensional analysis tips 1. Always include units. (remember a measurement always contains 2 parts: a number AND a unit) 2. Cancel units as you carry out your calculations 3. Check that your final answer has correct units 4. Check that your final answer has correct sig figs 5. Think about whether your answer makes sense. 37

Everyday examples Gas! Your gas tank holds 16 gallons. Gas is $3.11/ gal. at the nearest gas station. How much money are you going to have to collect from your couch to fill up your gas tank? 16 gal. x $3.11 gal. = $

Everyday examples If $1.00 is equal to euros. What is the value in $ of a 100 euro bill(Answer in 5 s.f.)? Apples cost $2.00 per lb. There are 8 apples in a lb. of apples. How many apples can you buy for $20? Text messages on Verizon are $.05/ txt. You typically text 120/ month. Verizon comes out with a plan for unlimited texts for 1 month that costs $5/month. Is this a good deal for you(Explain)? 39

Unit systems Metric: mass = kg English = ?? Metric: distance = meter English = ?? Metric: Volume = L, cm 3 English: Volume = ?? Metric: time = seconds (s) English: time=?? Metric: temperature= ?? English: temperature = ?? 40

Chapter 5 Density 41

objective and definitions Objective: To define density and its units Density: amt. of matter in a given volume D= mass/volume Mass in units of g volume in units of mL or cm 3 (L for gases) 1 mL = 1 cm 3 42

Density Density is the amount of matter present in a given volume of substance. It is the ratio of the mass of an object to its volume. Density = mass volume M D V This triangle can help you! Block the unit you need to solve for and the rest of the triangle will tell you how to get your answer. 43

Common units Common density units include: g/mL, g/cm 3, g/L (gases only). C.c. stands for cubic centimeter and is often used in the medical field. 1 cc=1mL 1 cm 3 = 1mL 44

Example problem You find that mL of a certain liquid weighs g. What is the density? g/mL 45

Water displacement One way to determine an object’s volume is a technique called water displacement. In this technique an object is submerged into a given volume of water. The change in volume is the object’s volume. 46

example A cube of metal weighs 1.45 kg and displaces 542 mL of water. What is the density of the metal? kg/mL 47

Density in the real world A material will float on the surface of a liquid if the material has a density less than that liquid. Which has a higher density water or ice? Fish don’t die in the winter!!!!! Which has a higher density Pb or water? 48