Practice Quiz Put the following in order from smallest to

largest. 1.8x10-5

8.7x1024

0.7x10-3

1.4x1040

Answers

Smallest Largest

1.8x10-5 0.7x10-3 8.7x1024 1.4x1040

Scientists (and those studying science) frequently must

deal with numbers that are very large or very small.

Instead of wasting time by writing many zeros before and after numbers, a method of writing

very large and very small numbers was invented. It is called scientific notation.

Rules

1) The first figure is a number from 1 to 9.

2) The first figure is followed by a decimal point and then the rest of the figures.

3) Then multiply by the appropriate power of 10.

Examples425=4.25x102 (102 is the same

as 100, so you are really multiplying 4.25 by 100)

0.00098=9.8x10-4 (10-4 is the same as 1/1000, so you are really multiplying 9.8 by 1/1000)

Practice

Write the following in scientific notation:

36000

0.0135

Try TheseTry to guess the answer without using

your calculator. 4.2x104kg + 7.9x103kg= 5.23x106mm x 7.1x10-2mm= 5.44x107g/8.1x104mol=

4.99x104kg3.7x105mm2

6.72x102g/mol

Metric System

Metric System Every measurement has two parts Number Scale (unit) SI system (le Systeme International) based

on the metric system Prefix + base unit Prefix tells you the power of 10 to multiply

by - decimal system -easy conversions

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The Fundamental SI Units

Prefixes giga- G 1,000,000,000 109

mega - M 1,000,000106

kilo - k 1,000 103

deci-d 0.1 10-1

centi- c 0.01 10-2

milli- m 0.001 10-3

micro- m 0.000001 10-6

nano- n 0.000000001 10-9

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The Prefixes Used in the SI System

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Some Examples of Commonly Used Units

Deriving the Liter Liter is defined as the volume of 1 dm3 gram is the mass of 1 cm3

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Measurement of Volume

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Soda is Sold in 2-Liter Bottles- an Example of SI

Units in Everyday Life

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Figure 1.7 Common Types of Laboratory Equipment Used to Measure Liquid

Volume

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Measurement of Volume Using a Buret

Mass and Weight Mass is measure of resistance to

change in motion Weight is force of gravity. Sometimes used interchangeably Mass can’t change, weight can

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Figure 1.8 An Electronic Analytic Balance

Significant Figures

Uncertainty Basis for significant figures All measurements are uncertain to

some degree Precision- how repeatable Accuracy- how correct - closeness to

true value. Random error - equal chance of being

high or low- addressed by averaging measurements - expected

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Figure 1.10 The Results of Several Dart Throws Show the Difference Between

Precise and Accurate

Neither accurate nor precise Precise but not accurate Both precise and accurate(large random error) (small random error, (small random error, large systematic error) no systematic error)

Uncertainty

Systematic error- same direction each time

Want to avoid this Better precision implies better accuracy you can have precision without accuracy You can’t have accuracy without

precision

Significant figures Meaningful digits in a MEASUREMENT Exact numbers are counted, have

unlimited significant figures If it is measured or estimated, it has sig

figs. If not it is exact. All numbers except zero are significant. Some zeros are, some aren’t

Rules

All non zero digits are significant

Ex: 127 Zeros between significant digits are always significant

Ex: 106 Leading zeros are never significant

Ex: 0.005 Trailing zeros are significant only if there is a decimal

Ex: 25.30

Copy the examples below and write the number of significant

figures1. 76231425162. 70843. 0.007614. 421.005. 0.5386. 50007. 5x103

8. 5.0 x103

9. 5000.10. 5120

Copy the examples below and write the number of significant

figures1. 7623142516 102. 7084 43. 0.00761 34. 421.00 55. 0.538 36. 5000 17. 5x103 18. 5.0 x103 29. 5000. 410. 5120 3

Which zeroes count? In between other sig figs does Before the first number doesn’t After the last number counts iff it is after the decimal point the decimal point is written in 3200 2 sig figs

3200. 4 sig figs

Multiplication and Division The final answer should have the same

number of sig figs as the measurement having the smallest number of sig figs

Ex: 10.305g x 0.00320g=

Ex: 3.64928g/5.2mL=

Addition and Subtraction Line the numbers up in column form

Ex: 3.461728+14.91+0.98001+5.2631=

Ex: 467.384-2.384=

Ex: 564321-264321=

Doing the math Multiplication and division, same

number of sig figs in answer as the least in the problem

Addition and subtraction, same number of decimal places in answer as least in problem.

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Rounding Numbers

Significant Figures Song

To the tune of Three Blind Mice

Verse 1 Addition and Subtraction line numbers

up in columns (Repeat) Make sure the decimals are aligned

right,

Take off the numbers that are on the right

To get the sig figs (Repeat)

Verse 2 Multiplication and division count the

numbers (Repeat) Find the one that is the least

That’s the number, the rest will cease To get the sig figs (Repeat)

Temperature

Temperature A measure of the average kinetic

energy Different temperature scales, all are

talking about the same height of mercury.

Derive a equation for converting ºF toºC

0ºC 32ºF

0ºC = 32ºF

ºC

ºF

(0,32)= (C1,F1)

100ºC 212ºF

100ºC = 212ºF

0ºC 32ºF

0ºC = 32ºF

ºC

ºF

(0,32) = (C1,F1)

(120,212) = (C2,F2)

100ºC 212ºF0ºC 32ºF

100ºC = 212ºF0ºC = 32ºF

100ºC = 180ºF

100ºC 212ºF0ºC 32ºF

100ºC = 212ºF0ºC = 32ºF

100ºC = 180ºF1ºC =

(180/100)ºF1ºC = 9/5ºF

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Figure 1.11 The Three Major Temperature Scales

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Figure 1.12 Normal Body Temperature

Equations

F=1.80(C)+32

C=(F-32)/1.80

Dimensional Analysis

Using the units to solve problems

Dimensional Analysis Use conversion factors to change the units Conversion factors = 1 1 foot = 12 inches (equivalence statement) 12 in = 1 = 1 ft.

1 ft. 12 in

2 conversion factors multiply by the one that will give you the

correct units in your answer.

Examples #1,2 11 yards = 2 rod 40 rods = 1 furlong 8 furlongs = 1 mile The Kentucky Derby race is 1.25 miles.

How long is the race in rods, furlongs, meters, and kilometers?

A marathon race is 26 miles, 385 yards. What is this distance in rods, furlongs, meters, and kilometers?

Example #3 Science fiction often uses nautical

analogies to describe space travel. If the starship U.S.S. Enterprise is traveling at warp factor 1.71, what is its speed in knots?

Warp 1.71 = 5.00 times the speed of light speed of light = 3.00 x 108 m/s 1 knot = 2000 yd/h exactly

Apothecaries (druggists) use the following set of measures in the English system:

20 grains ap = 1 scruple (exact) 3 scruples = 1 dram ap (exact) 8 dram ap = 1 oz. ap (exact) 1 dram ap = 3.888 g 1 oz. ap = ? oz. troy What is the mass of 1 scruple in grams?

Example #4

Example #5

The speed of light is 3.00 x 108 m/s. How far will a beam of light travel in 1.00 ns?

Group Practice

Group Practice-no flashcards1) Convert 0.049kg of sulfur to grams.

2) Convert 3µL of saline solution to liters.

3) Convert 150mg of aspirin to grams.

4) Convert 1.18dm3 to mL.

5) Convert 5230000nL of water to grams.

6) Convert 4.19L to cubic centimeters

7) Convert 310000cm3 of concrete to cubic meters

Complex Conversion Problems

#1

A heater gives off heat at a rate of 330kJ/min. What is the rate of heat output in kilocalories per hour? (1 cal=4.184J)

#1 Answer

4.7x103 kcal/h

#3

At the equator, Earth rotates with a velocity of about 465 m/s. What is the velocity in kilometers per hour? What is the velocity in kilometers per day?

#3 Answer

1670km/hr

4.02x104 km/d

#2

A water tank leaks water at the rate of 3.9mL/h. If the tank is not repaired, what volume of water in liters will it leak in a year?

#2 Answer

34L/yr

Density

Density Ratio of mass to volume D = m/V Useful for identifying a compound Useful for predicting weight An intrinsic property- does not depend

on what the material is

Formula Density=Mass/Volume D=m/V If you know the density triangle, you can

get the formulas for m and V. The units of density are always going to

have a division sign in them. Ex: g/mL

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Densities of Various Common Substances* at 20°

C

Example #1 An empty container weighs 121.3 g. Filled

with carbon tetrachloride (density 1.53

g/cm3 ) the container weighs 283.2 g. What is the volume of the container?

Example #2 A 55.0 gal drum weighs 75.0 lbs. when

empty. What will the total mass be when filled with ethanol?

density 0.789 g/cm3 1 gal = 3.78 L 1 lb = 454 g

Examples #3, 4, and 5(on your own)

3) Mercury has a density of 13.6g/mL. What volume of mercury must be taken to obtain 225g of the metal?

4) Isopropyl alcohol has a density of 0.785g/mL. What volume should be measured to obtain 20.0g of the liquid?

5) A beaker contains 725mL of water. The density of water is 1.00g/mL. Calculate the volume and mass of the water.

Answers

3) 16.5mL

4) 31.8mL

5) 0.725L, 0.725g