Scientific Notation, Metric(SI) Conversions, and ...



Scientific Notation, Metric(SI) Conversions, and Significant Figures

Scientific Notation:

In chemistry we use incredibly large and small numbers.

Scientific notation – a number between 1 and 10 raised to a power of 10.

Each time you move the decimal to the left, you are making the number ten times smaller you make the power of 10 one time larger.

100. = 1. x 10 x 10 OR 1 x 10 2

.001 = 1 x 1/10 x 1/10 x 1/10 OR 1 x 10 –3

1,230,600 move the decimal to make a number between 1 and 10 then raise the number to the correct power of ten.

When multiplying numbers written in scientific notation, multiply the coefficients and add the powers of ten.

5.0 x 10 4 3.0 x 102 7.0 x 10-6 2.0 x 10 -4

x 3.0 x 104 x 4.0 x 105 x 3.0 x 103 x 4.0 x 10 -6

When dividing numbers written in scientific notation, divide the coefficients and subtract the powers of ten.

6.0 x 10 4 3.5 x 102 7.0 x 10 6 8.0 x 10 -4

÷ 3.0 x 104 ÷ 7.0 x 105 ÷ 3.5 x 10 -3 ÷ 2.0 x 10 - 6

Addition and Subtraction:

Make the exponents the same then either add or subtract the coefficients and keep the exponent the same.

5.2 x 10 4 3.5 x 105 7.0 x 104 2.2 x 10 -4

+ 3.1 x 103 + 4.0 x 107 - 3.1 x 103 - 4.0 x 10 –5

International System (SI) of Units

Weight vs. Mass

Your Weight on the moon is 1/6 your weight on earth.

Your mass is the same regardless of the pull of gravity.

You can be weightless but you cannot be mass less.

France (1790), adopted internationally in 1960

Length – meter (m)

Volume – liter (L)

Mass –gram (g)

Temperature – Kelvin (K)

Energy – joule (j)

Time – second (s)

Pressure – pascal (Pa)

Amount of a substance – mole (mol)

Powers of 10 video.







Prefixes in front of base units Make the base unit powers of ten times as large.

Mega (M) = 1,000,000 (106) = 1 million

Kilo (K) = 1,000 (103) = 1 thousand

Deci (d) = 1/10 (10-1) = 1 tenth

Centi (c) = 1/ 100 (10-2) = 1 hundreth

Milli (m) = 1/ 1000 (10-3) = 1 thousanth

Micro ( ) = 1 / 1000000 (10-6) = 1 millionth

Nano (n) = 1/ 1000000000 (10-9) = 1 billionth

Pico (p) = 1 / 1000000000000 (10-12) = 1 trillionth

*** NOTE : 1cm3 = 1ml

Factor Label (dimensional analysis)

(Or proportions)

How many seconds are in one Year?

Convert 2.5 miles to inches (5,280 feet = 1 mile)

? How many meters are in 4.7 Km?

? How many Kg are in 3.77 mg??

?? How many ml are in .449 liters??

?? How many Megabites are in 47 Kb?

Convert the following units:

46 cm = _______m

3.77 x 105 ns = ______ s

.411 km = _________pm

35.6 g = ________kg

85 ml = _________ L

.573 mm =_______ cm

956 kg = _________ g

2.74 km =_________ m

.455 L = __________ ml

*How many cm3 are in 1m3 ? *

Accuracy, Precision and Error

*Every measurement involves error.

??? A student measures an object and is off by 5 microns (5 millionths of a meter), is the student very accurate or not ??

Radius of an atom = yes !!!

Radius of a car tire = no !!!

Accuracy - How close to the true or accepted value.

Precision – The repeatability of an experiment (how close a series of experiments are to one another)

Significant Figures

Every measurement involves error and uncertainty; the amount of error depends on the precision instrument used.

I.E. reading a thermometer that has graduations every 1 oC,

The most accurate temperature you could report (without giving more information than is true), is to the .1oC. Even though this is an estimated value it does have meaning (it is significant).

Determining the number of Significant figures a number has:

1.) All nonzero numbers are significant.

2.) Preceding Zeros: never count 0.000454 (3)

3.) Captive Zeros: Always count 5.1004 (5)

4.) Trailing Zeros: Only count when a decimal is present

3200

342.1000

Is there a difference between

4, 4.0, 4.00 and 4.000 ?

Lower Range Upper Range

4 3.5 4.4

4.0 3.95 4.04

4.00 3.995 4.004

4.000 3.9995 4.0004

2,031,004.20 (?)

0.00023040 (?)

0.130 (?)

• defined quantities and where only whole numbers could be present are two situations where unlimited number of sig. Figs are present. (12 inches in a foot, 5 people in your family etc.)

Adding and Subtracting

Round answer to the decimal place with the fewest decimal places, (not the number of digits)

5.2638 3.53215 7.052 9.2122

+ 3.14 + 4.031 - 3.1 - 4.031

Multiplication and division using Significant Figures

Round your answer to the number of significant figures as the value with the fewest number of significant figures.

6.0 3.00 9.0000 8.0 x 10 -5

x 3.000 x 7.0 ÷ 3.00 ÷ 2.00 x 10 5

??? A car gets 31.5 miles per gallon (mpg) of gas, how many miles can the car drive on 13.3 gallons of gas???

?? How many gallons of gas are needed to get the car from NYC to Florida? (trip = 1,455 miles) ???

If a car drives 322 miles on one tank of gas (12.7 gallons), how many miles per gallon is the car getting??

Percent Error

Percent Error = l experimental – accepted I x 100

Accepted

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1,500 people were expected to attend a concert, but only 1,350 turned up.

What was the percentage error?

? a student measures a length of Mg ribbon as 33.0 mm, later the length is determined to be 30.0mm.

What is the students percent error ?

?? A student determines the density of Chlorine gas at STP to be .0028 g/ml, what is the student’s % error ?

Potential Energy: Stored energy (energy of position).

Kinetic Energy: Energy of movement (motion).

(5-5) Temperature

Temperature - * * a measure of the average kinetic energy of the particles in the substance. * *

*** Any two substances that have the same temperature, have the same average kinetic energy

-**--- Heat always flows from body with higher temperature to body with lower temperature

Thermometer - instrument that measures heat content. (Liquid expands and contracts predictably as temperature changes)

°Celsius - based on two points:

F.P. / B.P. of water being 0 and 100 respectively.

Kelvin - (absolute scale) - has the same increments as celsius. **** Kelvin Temp is directly proportional to AVG. Kinetic Energy****

K = °C + 273 or °C = K - 273

zero K = theoretical lowest limit - have gotten to within .oo1 of a degree.

Use the above equations to convert the following:

1) 25 °C = K 2) 140°C = K

3) 0 °C = K 4) 273 °C= K

5) - 73 °C = K 6) 273 K = °C

7) 546 K = °C 8) 10 K = °C

??? is water heavy ??? What weighs more a pound of lead or a pound of feathers ?

Density

Is Steel more dense than water?

How does a Battleship float?

Density Mass of a substance that occupies a certain volume.

Density = mass/volume

g/ml (for solids + liquids)

g/l (for gasses)

Q. #1 The density of gold is 6.98 g/ml. What volume would be occupied by 700 g. of gold?

Q #2. 40.0 g. of a substance occupies 120 ml., what is the density of this substance?

Q # 3. What volume would be occupied by 20.0 g. of a substance with a density of 4.0 g/ml?

Q #4. The density of manganese is 7.21 g/ml, what mass of manganese would occupy 200 cm3 ?

Q #5. The density of air is 0.119 g/l. at 25°C. What volume would 50 g. air occupy?

Q # 6. If 30.0 g of a substance occupy 60. ml, what is the density of this substance?

Q #7. The density of lead is 11. g/ml, what mass of lead would occupy 44 ml?

Mass and Volume have a directly proportional relationship (Graph)

Introduction to Chemistry; Know For Test:

1) Scientific Notation

2) Metric System: conversions

3) Significant figures (I.D. how many, plus math)

4) Temperature: definition, K(-( °C, heat flow

5) Density

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