Ch. 2 Notes Day 4 Significant Figures

Objectives Define accuracy Define precision Compare accuracy & precision Use significant figures

Accuracy Accuracy refers to how closely a measurement matches the true or actual values To be accurate only requires the true value (bulls eye) & one measurement (for the arrow to hit the target) Highly accurate data can be costly and difficult to acquire

Precision Precision refers to the reproducibility of the measurement and exactness of description in a number. To decide on precision, you need several measurements (notice multiple arrow holes), and you do not need to know the true value (none of the values are close to the target but all the holes are close together.)

Accuracy & Precision In order to be accurate and precise, one must pay close attention to detail to receive the same results every time as well as “hit the target”.

Comparing Accuracy & Precision Notice the difference in these pictures. To win the tournament the archers must hit the target the most times. The winner must show accuracy & precision. The 1st archer has _____ accuracy & ____ precision. The 2nd archer has _____ accuracy & ____ precision. The 3rd archer has _____ accuracy & ____ precision. The 4th archer has _____ accuracy & _____ precision BAD BAD BAD GOOD GOOD GOOD GOOD BAD

Example 1 A sample is known to weigh 3.182 g. Jane weighed the sample five different times with the resulting data. Which measurement was the most accurate? 3.200 g 3.180 g 3.152 g 3.189 g

Example 2 Consider the data (in cm) for the length of an object as measured by three students. The length is known to be 14.5 cm. Which student had the most precise work, and which student had the most accurate work? Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Student A 14.8 14.7 Student B 14.2 14.6 Student C 14.4 14.5

Solution Most precise: Student A (0.1 cm difference) Most accurate: Student C (2 were true value, rest within 0.1 cm) Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Student A 14.8 14.7 Student B 14.2 14.6 Student C 14.4 14.5

Significant Figures Why are significant figures necessary? True accuracy is no better than the measurement obtained by the least precise method. We use significant digits so we are not exaggerating our precision.

Rules of Significant Digits All digits 1 through 9 are significant. 9.342 mg = 4 Sig. Digits 233,124 = 6 sig. digits

Rules of Significant Digits 2. Zero is significant when it is between two non‐zero digits 2.06 = 3 SD 206 = 3 SD 100,001 = 6 SD

Rules of Significant Digits 3. A zero to the right of a decimal point in a number greater than or equal to one is significant. 1.000 (4 SD) 30.00 (4 SD) 205.0 (4 SD) 2.00000 (6 SD) 10.0 (3 SD)

Rules of Significant Digits 4. A zero to the right of a decimal point (in a number less than one) but to the left of nonzero digit is not significant. 0.001020 (4 SD) 0.00024200 (5 SD)

Rules of Significant Digits 5. Zeros used only to space the decimal point (placeholders) are not significant. - 1000 (1 SD) - 1010 (3 SD) -78,000 (2 SD)

Counting SDs How many significant digits are in the following numbers? 235 1235 0.00010900 2020 65,100 235.0 19,620,000,000 0.0270 102, 800

Estimated to the tens place Estimated to the tenths place Why are S.F.s Important? When reporting a measurement the number of digits indicates the precision of an instrument. 100 ml Estimated to the tens place 99.9 mL Estimated to the tenths place

Example 1: How would you record this measurement? 1.37 cm

Example 2: Provide the measurements for each example. B.

How many significant digits would be recorded? 10 20 30 40 50 60 70 B. 10 20 30 40 50 60 70 C. 10 20 30 40 50 60 70

How many significant digits would be recorded? 48 cm (2 sfs) A. 10 20 30 40 50 60 70 B. 48 cm (2 sfs) 10 20 30 40 50 60 70 C. 48.0 cm (3 sfs) 10 20 30 40 50 60 70

What is a significant figure? There are 2 kinds of numbers: Exact: the amount of money in your account. Known with certainty.

What is a significant figure? Approximate: weight, height—anything MEASURED. No measurement is perfect.

When to use Significant figures When a measurement is recorded only those digits that are dependable are written down.

But, to a scientist 21.7cm and 21.70cm is NOT the same If you used an ordinary ruler, the smallest marking is the mm, so your measurement has to be recorded as 21.7cm.

How do I know how many Sig Figs? Rule: All non-zero digits are significant starting with the first non-zero digit on the left.

How do I know how many Sig Figs? Exception to rule: In whole numbers that end in zero, the zeros at the end are not significant.

How many sig figs? 7 40 0.5 0.00003 7 x 105 7,000,000 1

How do I know how many Sig Figs? 2nd Exception to rule: If zeros are sandwiched between non-zero digits, the zeros become significant.

How do I know how many Sig Figs? 3rd Exception to rule: If zeros are at the end of a number that has a decimal, the zeros are significant.

How do I know how many Sig Figs? 3rd Exception to rule: These zeros are showing how accurate the measurement or calculation are.

How many sig figs here? 1.2 2100 56.76 4.00 0.0792 7,083,000,000 2 4 3

How many sig figs here? 3401 2100 2100.0 5.00 0.00412 8,000,050,000 4 2 5 3 6

What about calculations with sig figs? Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers.

Add/Subtract examples 2.45cm + 1.2cm = 3.65cm, Round off to = 3.7cm 7.432cm + 2cm = 9.432 round to  9cm

Addition and Subtraction Count your numbers after the decimal, the one with the smallest amount after the decimal is how many your answer will have.

Multiplication and Division Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

Multiplication and Division The number with the least amount of significant figures is how many significant figures your answer will have

A couple of examples 75.8cm x 9.6cm = ? 56.78 cm x 2.45cm = 139.111 cm2 Round to  139cm2 75.8cm x 9.6cm = ?

Ch. 2 Notes Day 5 Dimensional Analysis

Objectives SWBAT convert between metric and other units SWBAT change unfamiliar units (given conversion factors) into familiar units to better qualitatively estimate solutions to problems

Dimensional Analysis Organized method of problem-solving Used in chemistry, physics, engineering, and medicine Communicates the path to scientists that follow your work Records your own path for your future use

The General Idea… Use known conversion factors to change units “step-by-step” until you end up with the units that you want. Common Conversion Factors 1 Day = 24 Hours 1 Inch = 2.54 cm 1 Hour = 60 Minutes 1 Minute = 60 Seconds 4 Quarts = 1 Gallon 1 Parsec = 3.62 Light Years 1 Yard = 3 Feet

Calculate the number of minutes in 3.61 hours. Dimensional Analysis Calculate the number of minutes in 3.61 hours. *Note: Use the number given in the question to determine the number of sig figs in your answer. 1. Write the given. 2. Draw the chart.

3. Think of a relationship: 1 hr = 60 min Dimensional Analysis Calculate the number of minutes in 3.61 hours. *Note: Use the number given in the question to determine the number of sig figs in your answer. 3. Think of a relationship: 1 hr = 60 min 4. Divide the relationship in ½ at the = sign. 5. Cancel units diagonally.

6. Add the rest of the relationship. Dimensional Analysis Calculate the number of minutes in 3.61 hours. *Note: Use the number given in the question to determine the number of sig figs in your answer. 6. Add the rest of the relationship. Count sig figs in the given. Round the answer to that number of sig figs.

How many centimeters are in 4.2 inches? Dimensional Analysis How many centimeters are in 4.2 inches? *Note: Use the number given in the question to determine the number of sig figs in your answer.

How many centimeters are in 4.2 inches? Dimensional Analysis How many centimeters are in 4.2 inches? *Note: Use the number given in the question to determine the number of sig figs in your answer.

Realize that we don’t know just one step from weeks to seconds. Dimensional Analysis Multi-Step Problems Calculate the number of seconds in two weeks. Realize that we don’t know just one step from weeks to seconds.

Dimensional Analysis Multi-Step Problems Start as usual. Calculate the number of seconds in two weeks. Start as usual.

Dimensional Analysis Multi-Step Problems Extend your table. Calculate the number of seconds in two weeks. Extend your table.

Continue adding relationships. Dimensional Analysis Multi-Step Problems Calculate the number of seconds in two weeks. Continue adding relationships.

Add as many conversions as needed. Dimensional Analysis Multi-Step Problems Calculate the number of seconds in two weeks. Round to 1 sig fig. Add as many conversions as needed.

Notice the use of the bottom space. Dimensional Analysis Multi-Step Problems Convert the density of 0.58 g/mL to lb/gallon. (1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb) Notice the use of the bottom space.

Ignore the bottom unit for a moment. Dimensional Analysis Multi-Step Problems Convert the density of 0.58 g/mL to lb/gallon. (1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb) Ignore the bottom unit for a moment. Concentrate on converting the top unit.

Continue converting the top. Stop when you get to lb…the goal. Dimensional Analysis Multi-Step Problems Convert the density of 0.58 g/mL to lb/gallon. (1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb) Continue converting the top. Stop when you get to lb…the goal.

Now, focus on the bottom units. Dimensional Analysis Multi-Step Problems Convert the density of 0.58 g/mL to lb/gallon. (1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb) Now, focus on the bottom units. It is OK to cancel units from a distance.

Continue adding until you reach the goal. Dimensional Analysis Multi-Step Problems Convert the density of 0.58 g/mL to lb/gallon. (1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb) Continue adding until you reach the goal.

If a pound of apples costs $0.79, then 5.3 lbs will cost _________. Fill-In iRespond Question If a pound of apples costs $0.79, then 5.3 lbs will cost _________. Give your answer to TWO decimal places which is customary with money. A.) 4.19;; B.) C.) D.) E.)

1849 yards = __________ miles Hint: 5280 ft = 1 mile Fill-In iRespond Question 1849 yards = __________ miles Hint: 5280 ft = 1 mile Give your answer to 4 sig figs. A.) 1.051;; B.) C.) D.) E.)

Give your answer to TWO sig figs. Fill-In iRespond Question If Boston and New York City are 190 miles apart, then the distance between the two cities is _______ km. Hint: 1 km = 0.621 miles Give your answer to TWO sig figs. A.) 310;; B.) C.) D.) E.)

Give your answer to THREE sig figs. Fill-In iRespond Question If a pound of apples costs $0.79, then a shopper with $2.00 will be able to purchase ________ lbs of apples. Give your answer to THREE sig figs. A.) 2.53;; B.) C.) D.) E.)

F Fill-In iRespond Question If a US car advertisement brags that an SVU gets 26 miles/gallon on the highway, then the same car would be described in Europe as getting ___________ km/L. Hint: 1 L = 1.057 qt; 4 qt = 1 gal; 1 km = 0.621 miles Give you answer to TWO sig figs. A.) 11;; B.) C.) D.) E.)