Measurement and Calculations

• Chemistry –

• Qualitative Measurement –

• Quantitative Measurement –

the science that deals with the materials of the universe and the changes these materials undergo

Qualities or observations that can be made about a substance ex: the substance is a yellow solid

a measurement that consists of a number and a unitex: the substance weighs 3.45 grams

Units• tells what scale or standard is being used to represent the measurement• International System (SI)• SI Base Units:

– Length:

• measures distance

– Mass:

• quantity of matter present in an sample

– Volume:

• 1 mL = 1 cm3

• three-dimensional space occupied by a sample

– Temperature:

• TK = T°C + 273

– Time:

– Pressure:

– Energy/Heat:

– Counting Atoms:

meter

grams

Liter, centimeter cubed, decimeter cubed

Kelvin, Celsius

secondPascals

Joules

moles

1 L = 1 dm3

Units

Common metric prefixes (MEMORIZE)Giga 1 x 109 _ = 1 G_Mega 1 x 106 _ = 1 M_Kilo - 1000 _ = 1 k_Hecto - 100 _ = 1 H_Deka - 10 _ = 1 D_(base) – meter, liter, gram…deci- 1 _ = 10 d_centi- 1 _ = 100 c_milli- 1 _ = 1000 m_micro- 1 _ = 1 x 106 _ ( = lowercase Greek Mu)nano- 1 _ = 1 x 109 n_pico- 1 _ = 1 x 1012 p_

*

***

*

Scientific Notation

Expresses a number as a product of a number between 1 and 10 and the appropriate power of 10

If you move the decimal point- left positive exponent right negative exponent

Ex: 200 g .00314 mL12

2 x 102 g 3.14 x 10-3 mL

1 2 3

Converting from Scientific Notation to Ordinary Numbers

move the decimal point-positive exponent right negative exponent

left

Ex: 6.32 x 101 cm 3.92 x 10-3 m1

63.2 cm

123

.00392 m

Learning Check

Try these:

1. 657000000000 m

2. 0.000000235 g

3. 9.34 x 102 cL

4. 3.35 x 10-3 L

6.57 x 1011 m

2.35 x 10-7 g

934 cL0.00335 L

Limits to Measurements• When measuring you should always

______________ the _______ digit of your measurement

• Your measurement should be recorded to ONE PLACE VALUE BEYOND the ______________marking

• Your Estimate (or _____________ number) should be the final one on the right.

• If the tool is digital, _________ the given number– no estimated number.

• Measurements always have some degree of uncertainty (estimation)

estimate last

calibrationuncertain

record

Ex 1: Measure the volume of liquid in the Graduated cylinder.

Remember: The volume is read at the bottom of the liquid curve (called the meniscus).

15.75 mL

7.5 cm

7.56 cm

Ex 2: Measure the line using both rulers.

Ex 3: Measure the volume of liquid in the buret.

42.8 mL

Learning checkRead the following pieces of equipment, record your

answer with the estimated digit and units.

1.

2.

3.

4.5.

Significant FiguresAll certain numbers plus first uncertain digit

Rules for counting Sig. Figs.

3. Exact numbers – have infinite number of sig. figs., they arise from definitions

c. Trailing Zeros – come at the end of a number and count IF there is a DECIMAL POINT

b. Captive (Trapped) Zeros – fall between two nonzero digits, they ALWAYS COUNT

2. Zeros a. Leading Zeros – precede all nonzero digits, they NEVER COUNT

1. All nonzero numbers are significant.3578 = 4 SF

236 = 3 SF

.0025 = 2 SF .0009 = 1 SF

6008 = 4 SF 20502 = 5 SF .00705 = 3 SF

3000 = 1 SF 3000. = 4 SF 2580.0 = 5 SF.001500300 = 7 SF

1 inch = 2.54 cm, 1 g = 1000 mg

Rounding

If the digit to be removed is –a. less than 5, the preceding digit stays the sameb. equal or greater than 5, increase the preceding digit

by 1When rounding off, use ONLY the first number to

the right of the last significant figure

Ex: Round to 3 SF

$ 10,079

0.002978 g

0.03296 cm

1000. mL

= $10,100

= 0.00298 g

= 0.0330 cm

= 1.00 x 103 mL

Learning Check

Determine the number of significant figures in the following numbers:a. 0.00340 g

b. 9.00 mm

c. 30.390 mL

Round each number to 2 significant figures.a. 0.00340 g

b. 9.00 mm

c. 30.390 mL

Calculations Notes

• Accuracy: - How _________ a measurement is to the actual or _________value. To evaluate accuracy you must __________ the true value. For example, knowing a watch is 5 min fast…The time on the watch is ________ accurate and you know it is not accurate b/c you know the real time and can make an ________.

• Shooting Free Throws - Accuracy can be measured by how many are __________.

Uncertainty in Measurement

closeaccepted

know

not

adjustment

baskets

Precision: 1st Meaning of PrecisionHow close a ____________ of measurements are to the

_________________. To evaluate precision you must compare the values of 2 or more _______________ measurements.

• Ex. Measure the temperature of water three times. Which set of measurements are more precise?

Thermometer 1: 22.3oC, 22.3oC, 22.4oCThermometer 2: 24.5oC, 20.1oC, 18.7oC

• Shooting Free Throws - Precision can be measured by how many _______ in the same _________. Ex. Consistently hitting the ___________ of the rim and missing. Not accurate b/c not making the shots, but precise b/c results are repeated.

• Science – should be both accurate (___________) and precise (can ____________ it consistently)

setactual value

similar

shots spotside

rightrepeat

2nd Meaning of Precision• Precision can also refer to how __________ a

measurement is (more decimal __________ = more precise)

Consider mass of sugar in bubble gum– 5 g - wide range of values that it could be! - Could be

between 4.5 g and 5.4 g and rounded to 5 g.– 5.0 g gives you more information – Could be between

4.95 g and 5.04 g.– 5.00 g gives you even more information – Could be

between 4.995 g and 5.004 g

• More numbers to ______________ of decimal, more precise the measurement is!

preciseplaces

right

Learning Check

Think of an example, from your life, of accuracy and precision.

Multiplication and Division

Number of the sig. figs. is the result of the measurement with the smallest number of sig. figs. (least accurate). LEAST NUMBER OF SIG FIGS!

Ex 1: 4.63 m x 7.5 m Ex. 2: 8.460 m2 / 2.1 m

34.725

35 m2

4.0285714286

4.0 m

3 sf 2 sf 4 sf 2 sf

Addition and Subtraction

Align the decimal points and carry out the calculation. First column from the left with an uncertain digit determines the number of sig. figs. in your answer (Chop & round at the GAP) LEAST NUMBER of DECIMAL PLACES!

Ex 1: 6.341 g + .789 g + 4.2 g Ex. 2: 6.799 m - 2.41 m

6.341 .7894.2

11.330

GAP11.3 g 6.799

2.414.389

GAP4.39 m

Learning Check

1. 22.4 L x 9.3 L

2. 9.63 g + 17.3251 g

Scientific Notation and Multiplication and Division

Multiplication – Multiply coefficients, ADD exponents, multiply units, round to proper S.F.

Division - Divide coefficients, SUBTRACT exponents, divide units, round to proper S.F.

Ex 1: (1.00 x 103 m)(3.2 x 102 m) Ex. 2: (3.00 x 104 g)/(1.0 x 102 cm3)

3.2 x 105 m2 3.0 x 102 g/cm3

Scientific Notation and Addition and Subtraction

must be in the same power of ten and same unit before you add or subtract coefficients, convert to larger exponent

Ex 1: 3.0 x 1023 m + 1.0 x 1022 m 1

3.0 x 1023 m + .10 x 1023 m

3.0 .103.10

GAP 3.1 x 1023 m

Learning Check

1. 2.29 x 105 g - 9.3 x 104 g

2. 6.02 x 1023 m ÷ 1.7 x 1022 m

Problem Solving and Dimensional Analysis

Conversion factor – ratio of two parts of the statement that relates the two units

Equivalence Statement – true statement in fraction form

Dimensional Analysis – when used properly all units will cancel out except the desired unit

2.54 cm = 1 inch

100 cm = 1 m

2.54 cm 1 inch

1 inch2.54 cm

100 cm 1 m

1 m 100 cm

or or

x ______________Desired UNIT

Wanted UNIT

#

#

x ________________

Wanted UNIT

#

#

Given UNIT

Given with UNITS=

Ex. 1: 250 m = ___________ km

Ex. 2: 3.54 g = ___________ mg

Ex. 3: 0.542 kg = __________ mg

x ___________km

1000

1

m

250 m = .25 km

x ___________mg

1

1000

g

3.54 g = 3540 mg

x __________mg

g

1000

1x ________g

1

1000

kg

0.542 kg = 542000 mg

1 km = 1000 m

1 g = 1000 mg

1 kg = 1000 g

1 g = 1000 mg

Learning Check

1. 0.542 mm = __________ km

2. 0.542 g = __________ µg

Determining Error

___________________value - correct value based on reliable references

___________________value - value measured in the lab

Error = experimental value – accepted value(Note: error can be positive or

negative) You will take the ___________ value of this when you calculate percent error.

accepted

experimental

absolute

Determining Percent (%) Error

Percent error = absolute value of error divided by accepted value and multiplied by 100%

% error = (experimental value – accepted value) x 100%accepted value

Example: You take three temperature readings of a beaker of boiling water and record: 91.3oC, 90.9oC, and 91.1oC. Evaluate accuracy, precision, and error. Accurate? No, water boils at 100oC

Precise? Yes, values are close to each other

1. Find average experimental data

2. Use formula

Error

(91.3oC + 90.9oC + 91.1oC)/3 = 91.1oC

% error = (91.1 oC – 100 oC) x 100%100 oC

= 8.90 %

Learning Check

1. At a track meet, you time a friend running 100 m in 11.00 seconds. The officials time her at 10.67 seconds. What is your percentage error?

For Fun!Hagrid instructed Harry to give the delivery owl five Knuts for a newspaper (p. 62). A weekday newspaper costs $0.25. At Gringots, Harry learned that there are seventeen Sickles to a Galleon and twenty-nine Knuts to a Sickle (p. 75). Harry then paid seven Galleons for his new wand-Holly and phoenix feather (p. 85). Use dimensional analysis to calculate how much Harry’s wand would cost in dollars?

On the train, Harry paid eleven Sickles and seven Knuts for junk food from the snack trolley. How much money did he spend?

x ___________ Galleon

Sickles17

1 x ___________

Sickles

Knuts 29

1

x __________Sickle

Knuts29

1

x ______________Knuts

dollars.25

5

x ___________ Knuts

dollars.25

5

7 Galleons $172.55=

=11 Sickles $ 15.95

x ___________

Knuts

dollars.25

5

7 Knuts = $ 0.35$16.30