Science Math

OBJECTIVES Precision VS Accuracy Rounding numbers Significant Figures Scientific Notation Metric Conversions Factor Label Method Temperature Conversions

DO NOW! Explain the difference between accuracy and precision.

DUCK QUESTIONS

TIP: Accuracy = Actual What is Accuracy? DEF: The accuracy of a measurement is how close a result comes to the true measurement. TIP: Accuracy = Actual

In the picture you see 4 darts are all close to the bulls eye but not to each other. They are ACCURATE because they are close

What is Precision? Precision is how well the values agree with each other in multiple tests.

Precision The 4 darts are not close to the bulls eye BUT they are all very close to each other.

ACCURATE AND PRECISE DARTS ARE ALL ACCURATE – because they are all in the bullseye DARTS ARE ALL PRECISE – Because they are all very close to EACH OTHER

ACCURATE AND PRECISE Measurements can most definitely be accurate and precise! This simply means that ALL of your measurements are close to the “correct” or “actual” measurement.

Accuracy VS Precision

HW Accuracy and Precision worksheet

Use the following words to describe each (2 labels each) Accurate/Inaccurate/Precise/Imprecise

HELLO! WARM UP Accuracy – how close your measurement is to the CORRECT value. Precision is how CONSISTENT your measurements are.

What is accurate?

Degree of Accuracy Example: Accuracy depends on the instrument we are measuring with. But as a general rule: The degree of accuracy is half a unit each side of the unit of measure Example:                                                                                     When an instrument measures in "1"s  any value between 6½ and 7½ is measured as "7"

Uncertainty – all measurements have uncertainty… +/- Set up a chart Put trials in TRIAL LENGTH 1 12.54 2 12.57 3 12.52 4 12.53 5 12.55

MEAN means AVERAGE Set up a chart Put trials in, find the MEAN (average) TRIAL LENGTH 1 12.54 2 12.57 3 12.52 4 12.53 5 12.55 MEAN (average)

 All measurements have a degree of uncertainty regardless of precision and accuracy.  Set up a chart Put trials in, find the MEAN (average) Take the highest value and subtract the lowest value (RANGE) then divide by 2 for Uncertainty in measurement. TRIAL LENGTH 1 12.54 2 12.57 3 12.52 4 12.53 5 12.55 MEAN (average) 12.57 – 12.52 = .05 .05 / 2 = .025 +/- uncertainty

What is precise? We will use % Error to identify precision.

Percent Error Percent Error is a way for scientists to express their uncertainty and error in measurement by giving a percent error. Kind of like the possible percent amount you may be wrong.

Defined % error = actual value-measured value X100 Actual value

Percent Error VIDEO REAL WORLD APPLICATION

% ERROR Actual – Measured Actual X 100 = % error

Percent Error

OBJECTIVES Precision VS Accuracy Rounding Numbers Significant Figures Scientific Notation Metric Conversions Factor Label Method Temperature Conversions

2.6 Rounding Off Numbers Often when doing arithmetic on a pocket calculator, the answer is displayed with more significant figures than are really justified. How do you decide how many digits to keep? Simple rules exist to tell you how. Chapter Two

VIDEO Grab your white boards – we are going to make sure you REMEMBER how to round correctly.

Round 286 to the nearest TEN Circle the tens spot – use the one to the right to determine if the ten spot goes up or down… It’s a 6 ….. SO it rounds up to 290

Try this one : Round 387,907 to the nearest hundred thousand: 387,907 Now round it to the nearest hundred…

Once you decide how many digits to retain, the rules for rounding off numbers are straightforward: RULE 1. If the first digit you remove is 4 or less, drop it and all following digits. 2.4271 becomes 2.4 when rounded off to two significant figures because the first dropped digit (a 2) is 4 or less. RULE 2. If the first digit removed is 5 or greater, round up by adding 1 to the last digit kept. 4.5832 is 4.6 when rounded off to 2 significant figures since the first dropped digit (an 8) is 5 or greater. If a calculation has several steps, it is best to round off at the end. Chapter Two

ROUNDING to SIGNIFICANT FIGURES is a way that scientists keep their numbers in check. It is a way to determine HOW MANY PLACES your answer should be rounded to. Remember last week…. Was it 4.1628 or 4.16 or 4.2 or 4? The idea is to round to the LEAST NUMBER OF SIGNIFICANT DIGITS that were given in the problem.

NOW>>>> which are significant? NOT ALL DIGITS ARE SIGNIFICANT… OF course – there are RULES!

Practice Rule #2 Rounding Make the following into a 3 Sig Fig number Your Final number must be of the same value as the number you started with, 129,000 and not 129 1.5587 .0037421 1367 128,522 1.6683 106 1.56 .00374 1370 129,000 1.67 106

Examples of Rounding For example you want a 4 Sig Fig number 0 is dropped, it is <5 8 is dropped, it is >5; Note you must include the 0’s 5 is dropped it is = 5; note you need a 4 Sig Fig 4965.03   780,582 1999.5 4965 780,600 2000.

RULE 1. In carrying out a multiplication or division, the answer cannot have more significant figures than either of the original numbers. Chapter Two

RULE 2. In carrying out an addition or subtraction, the answer cannot have more digits after the decimal point than either of the original numbers. Chapter Two

Multiplication and division 32.27  1.54 = 49.6958 3.68  .07925 = 46.4353312 1.750  .0342000 = 0.05985 3.2650106  4.858 = 1.586137  107 6.0221023  1.66110-24 = 1.000000 49.7 46.4 .05985 1.586 107 1.000

Addition/Subtraction 25.5 32.72 320 +34.270 ‑ 0.0049 + 12.5 59.770 32.7151 332.5 59.8 32.72 330

Addition and Subtraction Look for the last important digit .71 82000 .1 .56 + .153 = .713 82000 + 5.32 = 82005.32 10.0 - 9.8742 = .12580 10 – 9.8742 = .12580 __ ___ __

OBJECTIVES Precision VS Accuracy Rounding Numbers Significant Figures Scientific Notation Metric Conversions Factor Label Method Temperature Conversions

Significant Figures When using our calculators we must determine the correct answer; our calculators are mindless drones and don’t know the correct answer. Chapter Two

Significant Figures There are 2 different types of numbers Exact Measured

Exact Exact numbers are infinitely important A. Exact numbers are obtained by: 1. counting 2. definition

EXAMPLES: Exact Numbers Counting objects are always exact 2 soccer balls 4 pizzas **Exact relationships, predefined values, not measured 1 foot = 12 inches 1 meter = 100 cm For instance is 1 foot = 12.000000000001 inches? No 1 ft is EXACTLY 12 inches.

Measured (Inexact) Measured numbers are obtained by 1. using a measuring tool Measured number = they are measured with a measuring device so these numbers have ERROR.

Example: example: any measurement. If I quickly measure the width of a piece of notebook paper, I might get 220 mm (2 significant figures). If I am more precise, I might get 216 mm (3 significant figures). An even more precise measurement would be 215.6 mm (4 significant figures).

Remember Exact numbers you get by counting and definition. Inexact numbers you get by MEASUREMENT

QUESTION Check… do in notes Classify each of the following as an exact or a measured number. 1 yard = 3 feet The diameter of a red blood cell is 6 x 10-4 cm. There are 6 hats on the shelf. Gold melts at 1064°C.

SOLUTION 1 yard = 3 feet : EXACT: This is a defined relationship. 2. The diameter of a red blood cell is 6 x 10-4 cm. MEASURED: A measuring tool is used to determine length. 3. There are 6 hats on the shelf. EXACT: The number of hats is obtained by counting. Gold melts at 1064°C. MEASURED: A measuring tool is required.

QUESTION Check A. Exact numbers are obtained by 1. using a measuring tool 2. counting 3. definition B. Measured numbers are obtained by

Solution 2. counting 3. definition B. Measured numbers are obtained by A. Exact numbers are obtained by 2. counting 3. definition B. Measured numbers are obtained by 1. using a measuring tool

2.6 Rounding Off Numbers Often when doing arithmetic on a pocket calculator, the answer is displayed with more significant figures than are really justified. How do you decide how many digits to keep? Simple rules exist to tell you how. Chapter Two

VIDEO Grab your white boards – we are going to make sure you REMEMBER how to round correctly.

Try this one : Round 387,907 to the nearest hundred thousand: 387,907 Now round it to the nearest hundred…

Round 286 to the nearest TEN Circle the tens spot – use the one to the right to determine if the ten spot goes up or down… It’s a 6 ….. SO it rounds up to 290

Round 2,945,773 to the nearest million Hundred thousand Thousand Tens

Round 63.4956 to the nearest: Ten Tenth Hundredth Thousandth

Round 238456084.94765 to the nearest Hundred million Hundred One Thousandth

Once you decide how many digits to retain, the rules for rounding off numbers are straightforward: RULE 1. If the first digit you remove is 4 or less, drop it and all following digits. 2.4271 becomes 2.4 when rounded off to two significant figures because the first dropped digit (a 2) is 4 or less. RULE 2. If the first digit removed is 5 or greater, round up by adding 1 to the last digit kept. 4.5832 is 4.6 when rounded off to 2 significant figures since the first dropped digit (an 8) is 5 or greater. If a calculation has several steps, it is best to round off at the end. Chapter Two

ROUNDING to SIGNIFICANT FIGURES is a way that scientists keep their numbers in check. It is a way to determine HOW MANY PLACES your answer should be rounded to. Remember last week…. Was it 4.1628 or 4.16 or 4.2 or 4? The idea is to round to the LEAST NUMBER OF SIGNIFICANT DIGITS that were given in the problem.

Measured numbers in an answer that matter for reporting. Significant Figures Measured numbers in an answer that matter for reporting. Meant to make writing answers EASY! VIDEO

RULES

ALL NON ZERO’S ARE SIGNIFICANT Rule #1 ALL NON ZERO’S ARE SIGNIFICANT

Zeros in between significant digits are always significant. RULE 2. Zeros in between significant digits are always significant. Thus, 94.072 g has five significant figures.

RULE 2B. Zeros at the beginning of a number are not significant; they act only to locate the decimal point. Thus, 0.0834 cm has three significant figures, and 0.029 07 mL has four.

RULE 3. Zeros at the end of a number and after the decimal point are significant. It is assumed that these zeros would not be shown unless they were significant. 138.200 m has six significant figures. If the value were known to only four significant figures, we would write 138.2 m.

VIDEO Use the rules! Everytime!

Practice Rules ; Zeros – in your notebook 6 3 5 2 4 All digits count Leading 0’s don’t Trailing 0’s do 0’s count in decimal form 0’s don’t count w/o decimal 0’s between digits count as well as trailing in decimal form 45.8736 .000239 .00023900 48000. 48000 3.982106 1.00040

How many significant figures are in each of the following? 1) 23.34 4 significant figures 2) 21.003 5 significant figures 3) .0003030 4 significant figures 4) 210 2 significant figures 5) 200 students 1 significant figures 1 significant figures 6) 3000

HOMEWORK : ID SIG FIGS Practice ! Practice! Chapter Two

FUNctions with sig figs

ADD AND SUBTRACT SIG FIGS! Add and subtract accordingly – always use the LEAST AMOUNT OF SIGNIFICANT FIGURES AFTER THE DECIMAL!

Using Significant Figures in Calculations Addition and Subtraction Line up the decimals. Add or subtract. Round off to first full column. 23.345 +14.5 + 0.523 = ? 23.345 14.5 + 0.523 38.368 = 38.4 or three significant fingures

EXAMPLE 38.2567896563 g + 26943.54 g 38.2567896563 + 26943.54 g ______________________ 26981.7967896563 26981.80 Final Answer

HOMEWORK : ADD AND SUBTRACT Practice ! Practice! Chapter Two

MULTIPLY AND DIVIDE! YEAH!

Using Significant Figures in Calculations Multiplication and Division Do the multiplication or division. Round answer off to the same number of significant figures as the least number in the data. (23.345)(14.5)(0.523) = ? 177.0368075 = 177 or three significant figures

DO HW SHEET! MULTIPLY AND DIVIDE Practice ! Practice!

OBJECTIVES Precision VS Accuracy Significant Figures Scientific Notation 1 Metric Conversions Factor Label Method Temperature Conversions

DO NOW! Put 215 into scientific notation

2.5 Scientific Notation Scientific notation is a convenient way to write a very small or a very large number. Numbers are written as a product of a number between 1 and 10, times the number 10 raised to power. 215 is written in scientific notation as: 215 = 2.15 x 100 = 2.15 x (10 x 10) = 2.15 x 102 Chapter Two

Scientific Notation Scientists have developed a shorter method to express very large numbers. This method is called scientific notation. Scientific Notation is based on powers of the base number 10.

UNDERSTANDING SCIENTIFIC NOTATION

Scientific Notation The number 145,000,000,000 in scientific notation is written as : 1.45 X 1011 The first number 1.45 is called the coefficient. It must be greater than or equal to 1 and less than 10. The second number is called the base . It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.45 x 1011 the number 11 is referred to as the exponent or power of ten.

To write a number in scientific notation: If the number 123,000,000,000 Put the decimal after the first digit and drop the zeroes. The coefficient will be 1.23 To find the exponent count the number of places from the decimal to the end of the number. In 123,000,000,000 there are 11 places. Therefore we write 123,000,000,000 as:

ANSWER 1.23 X 10 11

King Henry Doesn’t Usually Drink Chocolate Milk Kilo Hecto Deka UNIT Deci Centi Milli 1,000 100 10 1 .1 .01 .001 If you move LEFT from the decimal exponent goes UP IF you move RIGHT from the decimal exponent goes DOWN

Scientific Notation VIDEO Worksheet Fix Incorrect

Operations w scientific notation

Exponent Rules To multiply exponents = add exponent To Divide exponents = subtract exponent VIDEO

DO WORKSHEET http://lasp.colorado.edu/~bagenal/MATH/problems/problems1.html answers

OBJECTIVES Precision VS Accuracy Rounding Numbers Significant Figures Scientific Notation Metric Conversions Factor Label Method Temperature Conversions

METRIC SYSTEM What everyone else in the world uses. Based on multiples of 10. Called the “International System of Units” or SI for short. VIDEO

Who uses it? Not Metric ; Liberia, Myanmar (Burma) and the United States (black)

Metric System The United States is the only industrialized country that does not use the metric system as its official system of measurement, although the metric system has been officially sanctioned for use here since 1866. VIDEO

Measurement in Chemistry Length Mass Volume Time meter gram Liter second Km=1000m Kg=1000g KL=1000L 1min=60sec 100cm=1m 1000mg=1 g 1000mL=1L 60min=1hr 1000mm=1m SI System Foot pound gallon second British 12in=1ft 16oz=1 lb 4qt=1gal (same) 3ft=1yd 2000 lb=1 ton 2pts=1qt 5280ft=1mile

Metric to Metric Conversion VIDEO

King Henry Doesn’t Usually Drink Chocolate Milk 1,000 Kilo 100 Hecto 10 Deka UNIT Meters, Liters and Grams VIDEO 0.1 Deci 0.01 Centi 0.001 Milli

Do Practice Problems http://sciencespot.net/Media/metriccnvsn2.pdf Wksht / answers

OBJECTIVES Precision VS Accuracy Rounding Numbers Significant Figures Scientific Notation Metric Conversions Factor Label Method Temperature Conversions

SI Prefixes Multiple Prefix Symbol 106 mega M 103 kilo k 10-1 deci D 10-2 centi C 10-3 milli m 10-6 micro 10-9 nano n 10-12 pico p 2

Relationships of Some U.S. and Metric Units Length Mass Volume 1 in = 2.54 cm 1 lb = 0.4536 kg 1 qt = 0.9464 L 1 yd = 0.9144 m 1 lb = 16 oz 4 qt = 1 gal 1 mi = 1.609 km 1 oz = 28.35 g 1 mi = 5280 ft 1 L = 1.06 qt 1 lb = 454 g 2

One Step Conversions

Feet to Inches So using that set up how many inches in 3 feet? Hours in a day? Feet in a mile?

Multiple Step Conversions

Factor Label Method How many Years have you been alive? Days? Seconds?

Units: Dimensional Analysis The ratio (3 feet/1 yard) is called a conversion factor. 2

TIPS 1. Start simple. 2. Write units with your numbers ALWAYS! 3. Go step by step. 4. Check your conversion factors. 5. Pinpoint what the question is asking 6. Is your answer logical? 7. Practice, practice, practice.

Worksheet VIDEO Video

OBJECTIVES Precision VS Accuracy Rounding Numbers Significant Figures Scientific Notation Metric Conversions Factor Label Method Temperature Conversions

Temperature The Fahrenheit scale is at present the common temperature scale in the United States. The conversion of Fahrenheit to Celsius, and vice versa, can be accomplished with the following formulas: C to F : C 9/5 +32 = F F to C : (F-32) 5/9 = C 2

Figure 1.23: Comparison of Temperature Scales

Temperature The Celsius scale (formerly the Centigrade scale) is the temperature scale in general scientific use. However, the SI base unit of temperature is the kelvin (K), a unit based on the absolute temperature scale. The conversion from Celsius to Kelvin is simple since the two scales are simply offset by 273.15o. 2