take out materials for notes – believe me, you’ll want to take them

Take out materials for notes – believe me, you’ll want to take them

Significant figures = important numbers

0.01 vs. 0.010 vs. 0.0100Which number is more precise?

Deals with measured or computed values (as opposed to exact values like 2 eyes, 12 eggs)

To what place can we record measurements on this graduated cylinder?• It is given to the ones

place, so we estimate to the tenths place

• Sig figs explain why 50 mL is not the same as 50.0 mL

RULE 1: All nonzero digits are significant:

RULE 2: Zeroes between nonzero digits are significant.

RULE 3: Leading zeros to the LEFT of the first nonzero digits are NOT significant; such zeroes merely indicate the position of the decimal point.

RULE 4: Trailing zeroes that are also to the RIGHT of a decimal point in a number ARE significant.

RULE 5: When a number ends in zeroes that are not to the right of a decimal point, the zeroes are NOT necessarily significant

515 3 sig figs 5050 3 sig figs 0.5050 4 sig figs 0.05050 4 sig figs 5000 1 sig fig 0.0500 3 sig figs 505.0 4 sig figs

Based on these

Can you guess how many are in the following #s?

43011.050.5680.0079812000

1.Figure out which side of the number to start from (Absent or Present)

2.Start counting at your first non-zero number

3.KEEP COUNTING!!!

If digit next to last significant figure is:0-4 don’t round 5-9, then round up

12488 (3 sig figs) 0.008209 (2 sig figs)

2.77549 (4 sig figs) 0.352 (1 sig fig)

Make sure your new rounded number is close to your original number!!!!

Adding/subtracting – line up the numbers, add ‘em up, and cut off at the shortest tail (round if necessary)

3.31 + 12.565 + 25.0915

147.3 + 29.12 + 0.115

178.1 – 92.67

1505.22 – 500

Count number of sig figs in each of your numbers – the lowest number of sig figs is the number of sig figs that will be in your answer

32.7 x 2.5 19.9 x 100

135.5 5.7 281 9.341

3.461728 + 14.91 + 0.980001 + 5.2631

0.04216 - 0.0004134

2.3 x 3.45 x 7.42 =  

208 / 9.0 =   

Calculate, using sig figs

0.00783 + 0.022 + 1.057

225.112 ÷ 14.78

Record your answer using the correct number of significant figures and proper units.

a. 7.55 m x 0.34 m _____

b. 2.10 m x 0.700m ____

c. 2.4526 m / 8.4 sec_____

d. 0.365 m / 0.0200 hr _____

e. 8432 m / 12.5 hr _____

f. 7 m x 1.22 m ____

A student once needed a cube of metal that had to have a mass of 83 grams. He knew the density of this metal was 8.67 g/mL, which told him the cube's volume. Believing significant figures were invented just to make life difficult for chemistry students and had no practical use in the real world, he calculated the volume of the cube as 9.573 mL. He thus determined that the edge of the cube had to be 2.097 cm. He took his plans to the machine shop where his friend had the same type of work done the previous year. The shop foreman said, "Yes, we can make this according to your specifications - but it will be expensive."

"That's OK," replied the student. "It's important." He knew his friend has paid $35, and he had been given $50 out of the school's research budget to get the job done.

He returned the next day, expecting the job to be done. "Sorry," said the foreman. "We're still working on it. Try next week." Finally the day came, and our friend got his cube. It looked very, very smooth and shiny and beautiful in its velvet case. Seeing it, our hero had a premonition of disaster and became a bit nervous. But he summoned up enough courage to ask for the bill. "$500, and cheap at the price. We had a terrific job getting it right -- had to make three before we got one right."

"But--but--my friend paid only $35 for the same thing!" "No. He wanted a cube 2.1 cm on an edge, and your

specifications called for 2.097. We had yours roughed out to 2.1 that very afternoon, but it was the precision grinding and lapping to get it down to 2.097 which took so long and cost the big money. The first one we made was 2.089 on one edge when we got finished, so we had to scrap it. The second was closer, but still not what you specified. That's why the three tries."

Oh!"

You’ll be going to each graduated cylinder and triple beam

Record the number graduated cylinder and its volume (be sure to estimate an extra place)

Record the letter of the triple beam, and find the mass of the object (be sure to estimate an extra place)

Be sure to use sig figs in your answers!

2 + A - 1 =

B ÷ 3 =

4 x D ÷ C =

If you don’t have one, I have ones in the box at the front – just sign one out

Warm up:Calculate, using sig figs

25.978 + 5.901 + 139.8

250 ÷ 9.25

Write the following numbers in scientific notation:

840,00035000.00007850.008812

Perform function with base numbersMultiplying = add exponentsDividing = subtract exponents

Putting answer in correct scientific notation:decimal Left = exponent Larger decimal Right = exponent Reduced

(2.0 x 10 -1) x (8.5 x 105)

(4.42 x 10-3) x (4 x 10-2)

(9.4 x 10 2) (1.24 x 10-5)

(9.2 x 10-3) (6.3 x 106)     

Now let’s learn about the EE

button!

(2.5 x 102 ) + (5.2 x 104 )

(4.1 x 103) + (3.25 x 102)

(9.86 x 104) - (1.2 x 102)

How many sig figs should be in each answer?

Calculate, using the EE button

Addition/Subtractioni) 4.01 x 10-9

j) 9.4 x 1010

k) -2.8 x 107

l) 4.62 x 10-1

m) 2.5 x 106

n) 6.6 x 1018

Multiplication/Division8) 2.6 x106

9) -1.31 x 1014

10) 3.74 x 10-9

11) -2.1 x 1016

12)-8.9 x 1020

13) 4.3 x 1016

14) 1.4 x 1045

Calculate, with correct number of sig figs:

8.56 x 0.030 x 12.15

(198.1 – 7.82) / 2.5

Accuracy = measurements are close to the given, accepted value

Precision = getting the same measurement each time; also pertains to the number of places you use in a measurement

9.52 cm is more precise than 9.5 cm

If I said I was 6 feet, 5 inches, 2.38 cm tall, I would be ________________ but not _________________.

A way to report how far off your values were from the accepted value

The closer you are to 0%, the better your results

|measured - accepted| x 100

accepted

A student measures the volume of a 2.50 liter container to be 2.38 liters. What is the percent error in the student's measurement?

Don’t forget about sig figs!

4.8% error

Carefully read and follow the instructions

Percent error calculations – use absolute value

| 5.00 – measure | x 100 5.00

The melting point of a chemical is 53.0oC. In a lab, two students try to verify this value. The first student records 51.5oC, 53.5oC, 55.0oC and 54.2oC. The second student records 52.3oC, 53.2oC, 54.0oC and 52.5oC.

1. Calculate the average value for each student2. Calculate the % error for each average3. Which student is most precise? Most accurate? How do you know?

Celsius or Kelvin

0 Co = 273 K Guess how you 10 Co = 283 K 100 Co = 373 K solve for Kelvin

Fahrenheit to Celsius is a little harderFo = 1.8(Co) + 32

Convert 60o C to Kelvin

Convert 75o F to oC

Convert 323 K to oC

Convert 10o C to oF

Convert 90o F to K

Convert 400 K to oF

Chocolate chip cookies:1 sugar1 brown sugar1 ½ butter2 ½ all purpose flour½ salt1 baking soda2 semisweet chocolate chips

SI Units – Systeme Internationale d’UnitesA universal system of measurement that allows people all over to discuss and trade without confusion

kilogram = kilogram

Time Length Mass Temperatur

e Amount of a

substance

Second (s)Meter (m)Kilogram (kg)Kelvin (K)mole (mol)

The standard kilogram kept in a vacuum sealed container in France.

An SI unit that is defined by a combination of base units

Density = g/mL Volume = cm3

If you know the units, you can figure out the formula, or vice versa

What is the unit for speed? What is the formula for speed then?

A way of converting from one unit to another

Conversion factors1 min = 60 sec12 in = 1 foot16 oz = 1 lb

Convert the following using the provided formulas:

65 oF to oC

393 K to oF

Formulas:K = oC + 273

oF = 1.8(oC) + 32

Convert:• 45 inches to miles1. Start with your given2. Figure out which conversion factors you

need3. Set it up so units cancel4. Do the calculations

Multiply across the top, divide across the bottom

• 3.6 miles to centimeters

• 1450 minutes to days

• 0.8 days to seconds

• 1.3 x 1010 seconds to years

WARM-UPWARM-UP

Using dimensional analysis, solve the following:

If 25 zags = 1 zangdoodle, and 3.5 zangdoodles = 1 raz, and 1.75 raz = 1 zoom, how many zags would you have if you had 8.9 zooms?

Warm up:Convert 450.0 oz to tons

1 ton = 2000 lbs 1 oz = 28.3 g

1 pound = 454 g

Let’s rewrite our answers with sig figs!

Only base the number of sig figs off of the given, NOT the conversion factors

The average student is in class 330 min/day.

a.How many hours/day is the average student in class?

What is changing? What conversion factors do I need?

b. How many seconds is the average student in class per week?

How many mph is 23 km/hr?

How many mph is 459 ft/sec?

How many ft/hr is 4515 cm/min?

Why does the tiny golf ball sink, and the much larger bowling ball floats?

What 2 things does density take into consideration?

What is the unit for density? (You can figure this out from the formula)What units must you be in to calculate density?

Density = Mass/VolumeVolume = l x w x h

1 m = 100 cm = 1000 mm1 km = 1000 m

1 inch = 2.54 cm

1 lb = 16 oz1 lb = 454 g

An oddly shaped piece of iron has a mass of 45.8 g. A graduated cylinder contains 35.0 mL of water. After dropping the iron in to the water, the level rises to 43.6 mL. What is the density of iron?

What do these 3 blocks have the same amount of? Volume

Which one has more “stuff” in it?

Which is the least dense? Most dense?

If you were to draw what the atoms look like in each of the blocks, what would they look like?

Why does the candle sink more in one of the graduated cylinders than in the other?

Something will float if it is (more, less) dense than the substance it is in.

Rank the densities of the liquids in relation to the candle

Warm up:If the following items were combined (and

did not mix) put them in order from top to bottom

densitiesalcohol 0.79 g/mLcorn syrup 1.36 g/mLdishwashing liquid 1.03 g/mLvegetable oil 0.9 g/mLrubber stopper 1.5 g/cm3

cork 0.2 g/cm3

Using the provided equipment (and water from the sink), find and record the mass and volume of 4 different amounts of water

Be sure to use an estimated digit in your measurements

Make sure you are finding the mass of just the water

From your data, calculate the density for each sample• Be sure to use sig figs!

Calculate the average density

The actual density of water is 1.00 g/mL. Calculate your percent error

Do you think both will sink or float in water?

Without dropping them in water, how could you figure this out?

Something will float if it is (more, less) dense than the substance it is in.

An object has a mass of 35.0 grams.  On Huey’s balance, it weighs 34.92 grams.  What is the percent error of his balance? 

The Handbook of Chemistry and Physics lists the density of a certain liquid to be 0.7988 g/mL.  Fred experimentally finds this liquid to have a density of 0.7914 g/mL.  The teacher allows up to +/- 0.500% error to make an “A” on the lab.  Did Fred make an “A”?  Prove your answer.

Each of five students used the same ruler to measure the length of the same pencil. These data resulted: 15.33 cm, 15.34 cm, 15.33 cm, 15.33 cm, 15.34 cm. The actual length of the pencil was 15.85 cm. Describe whether accuracy and precision are each good or poor for these measurements.

A chemistry student measured the boiling point of naphthalene (C10H8) at 231.0°C. What is the percent error for this measurement if the literature value is 217.9°C?