Measurements & Calculations

Chapter 2

SCIENTIFIC NOTATION

Section 2.1

Objective: show how very large or very small numbers can be expressed as the product of a number between 1 and 10 AND a power of 10

In science, we often encounter very large and very small numbers. Using scientific numbers makes

working with these numbers easier

RULE 1As the decimal is moved to the left

The power of 10 increases onevalue for each decimal place moved

Any number to theZero power = 1

RULE 2As the decimal is moved to the right

The power of 10 decreases onevalue for each decimal place moved

Any number to theZero power = 1

UNITS and MEASUREMENTS OF LENGTH, VOLUME & MASS

Section 2.2 and 2.3

Objective: to learn english, metric and SI systems of measurement

MEASUREMENTS OF LENGTH, VOLUME & MASS

Section 2.3

Objective: understand metric system for measuring length, volume and mass

SIGNIFICANT FIGURES

Section 2.5

Objective: to learn how to determine the number of sig figs

Significant Figures All number other then zero are significant

Ex. 23 = 2 sig figs Leading zeros- zeros that are at the beginning of a number are

NEVER significant Ex 034 = 2 sig figs and .0578 = 3 sig figs

Trapped zeros – zeros that are trapped between two other significant figures are ALWAYS significant Ex 304 = 3 sig figs and 8.0091 = 5 sig figs

Trailing zeros – zeros that are at the end of a number – depends on if there is a decimal point expressed in that number If there is a decimal point showing in the number then the

zeros are significant Ex 60 = 1 si fig but 60. = 2 sig figs and 60.0 = 3 sig figs Ex .05 = 1 sig figs

If there is NOT a decimal point showing in the number then the zeros are NOT sinificant

Example: 120000

120000.

No decimalpoint

Zeros are not significant!

2 sig figs

DecimalPoint

All digits includingzeros to the left ofThe decimal are

significant. 6 sig figs

Zeros betweenNon zeros are

significant

All figures areSignificant4 sig figs

Zero to theRight of theDecimal aresignificant

All figures areSignificant5 sig figs

Zeros to the right ofThe decimal with no

Non zero values Before the decimalAre not significant

3 sig figs

Zeros to the right of the decimalAnd to the right of non zero values

Are significant

5 sig figs

Exact equivalences have an unlimited number of significant figures

Therefore in the statement 1 in = 2.54 cm, Neither the 1 nor the 2.54 limits the number of

Sig figs when used in a calculation

The same is true for:

Exact numbers (numbers that were not obtained using measuring

devices, but determined by counting) also have an unlimited number of sig figs

Examples: 3 apples

8 molecules32 students

UNCERTAINTY IN MEASUREMENT

Section 2.4

Objective: to understand how uncertainty in measurement arisesDifference between accuracy and precision

Significant figures are used to distinguish truly measured values from those simply resulting from calculation. Significant figures determine the precision of a measurement. Precision refers to the degree of subdivision of a measurement.

As an example, suppose we were to ask you to measure how tall the school is, you replied “About one hundred meters”. This would be written as 100 with no decimal point included. This is shown with one significant figure the “1”, the zeros don’t count and it tells us that the building is about 100 meters but it could be 95 m or even 104 m. If we continued to inquire and ask you to be more precise, you might re-measure and say “ OK, ninety seven meters. This would be written as 97m. It contains two significant figures, the 9 and the 7. Now we know that you have somewhere between 96.5m and 97.4m. If we continue to ask you to measure even more precise with more precision, may eventually say, “97.2 m”.

THE PRECISION OF YOUR MEASUREMENT IS DICTATED BY THE INSTRUMENT YOU ARE USING TO MEASURE!!!!

Significant Figures

ACCURACY MEANS HOW CLOSE A MEASUREMENTIS TO THE TRUE VALUE

PRECISION REFERS TO THE DEGREE OFSUBBDIVISION OF THE MEASUREMENT

FOR EXAMPLE, IF A ROOM IS 10 FEET LONG ANDYOU MEASURE IT TO BE 15.9134 FT LONG, YOUR

MEASUREMENT IS VERY PRECISE BUT INACCURATE !

MEASUREMENTS SHOULD BE ACCURATE AND ASPRECISE AS THE MEASURING DEVICE ALLOWS

Illustration of accurate vs percise

You tell me. What is it?

1 2 3 4 5 6 7

Measurements are always all measured values plus one approximated value. The pencil is 3.6 cm long.

3 4

With more calibration a more precise measurement is possible

The pencil is 3.64 cm long!

3.6 3.7

Now 3.640 cm !The calibration of the instrument

determines measurement precision

What is the precision on a ruler?

Follow directions from Mrs McGrath & try to figure it out???

What if your measurement was in cm? What if your measurement was in mm?

Scales and sig figs

In our class Write down what the

scale says Most scales are taken

to the hundreths place

Graduated Cylinders & Thermometers

First – figure out scale Then – take measurement out to one guess past certainity

MATH AND SIG FIGSSection 2.5 continued

RULES FOR ROUNDING OFFRound each number to one sig fig:

If the digit is to be removed:

Is less than 5, the preceding digit stays the same

EX. 1.49 rounds to ???? _____________

is equal to or greater then 5, the preceding digit is increased

EX. 1.509 rounds to ???? _____________

In calculations: carry the extra digits through to the final result AND THEN round off

Addition/Subtraction with Sig Figs

Adding and subtracting with significant figures. The position, not the number, of the significant

figures is important in adding and subtracting. For example,

12.03 (the last sig fig is in hundredth place (0.01))

+ 2.0205 (the last sig fig is in ten thousandth (0.0001))

14.0505 14.05 (the answer is rounded off to

the least significant position hundredths place)

The numbers inthese positions arenot zeros, they are

unknown

Don’t even look at The 6 to determineRounding. Only

Look at the 4The answer is rounded to theposition of least significance

Multiplying/Dividing with Significant Figures

The result of multiplication or division can have no more sig figs than the term with the least number. *ex. 9 x 2 = 20 since the 9 has one sig fig and the 2 has one sig fig, the answer 20 must have only one and is written without a decimal to show that fact. * By contrast, 9.0 x 2.0 = 18 each term has two sig figs and the answer must also have two.

*4.56 x 1.4 = 6.384 How many sig figs can this answer have? 6.4 (2 sig figs)

DIMENSIONAL ANALYSIS

Section 2.6

Objective: learn how to apply dimensional analysis to solve problems

NO KING HENRY

You must use dimensional analysis to convert from metric to metric

You must use your brain and logic to do this

K H D b d c m

From the last slide we learned the meaning of some of the common prefixes, BUT we are going to learn to dimensional analysis using the root prefixes and deciding bigger/smaller.

Conversions YOU Need to Memorize Length

1in = 2.54 cm39.37 in = 1 meter1 mile = 5280 feet

Mass1kg = 2.2 lbs1lb = 454 grams

Volume1 liter = 1.06qts1 gallon = 3.79 liters

Dimensional Analysis Rules

1.37days = ? minutes Always start with the known value over the

number 1 Always write one number over the other Always, Always, Always, Always, Always

write/include the unit with the number 1.37 days

1

Single step

examples 3.6 m = ? ft 6.07 lb = ?kg 4.2 L = ?qt 35.92 cm = ? in

Equivalence statements Length

1in = 2.54 cm 39.37 in = 1 meter 1 mile = 5280 feet

Mass 1kg = 2.2 lbs 1lb = 454 grams

Volume 1 liter = 1.06qts 1 gallon = 3.79 liters

Double step

Exampls 56,345 s = ? yrs 98.3 in = ?m 3.2 mi = ?km

Equivalence Statements Length

1m = 1.094 yd 2.54 cm = 1 in 1mi = 1760 yd

Mass 1kg = 2.205 lb 453.6 g = 1lb

Volume 1 L = 1.06qt

TEMPERATURE CONVERSIONS

Section 2.7

Objective: to learn three temperature scales to convert from one scale to another

Temperature – the average kinetic energy in a substance Boiling points

Fahrenheit 212 F Celsius 100 C Kelvin 373 K

Freezing points Fahrenheit 32 F Celsius 0 C Kelvin - 273 K

*O Kelvin or Absolute zero: point at which molecular motion stops

Temperature Conversion Formulas

Celsius to Kelvin TK = TC + 273

Kelvin to Celsius TC = TK – 273

Celsius to TF = 1.80TC + 32Fahrenheit

Fahrenheit to TC = TF - 32Celsius 1.80

DENSITY

Section 2.8

Objective: to define density and its units

Density: the amount of matter present in a given volume of a substance

Formula Density = mass/volume

Units Density = g/ml OR g/cm3

Mass = g (grams) Volume = ml OR cm3

Liquids OR solidsDENSITY of a substance never changesEx gold is ALWAYS 19.3g/cm3

Less dense objects “FLOAT” in more dense objects

Example calculation

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

Example calculation: ANSWER

Mercury has a density of 13.6g/ml. What volume of mercury must be taken to obtain 225 grams of the metal? 16.5 mL

THE END