measuring. what are significant figures any digit of a number that is known with certainty. they...
TRANSCRIPT
Measuring
What are Significant Figures Any digit of a number that is known with Any digit of a number that is known with
certainty. They tell you how precise a certainty. They tell you how precise a measurement is.measurement is.
Recording Sig FigsRecording Sig Figs Sig figs in a measurement include the known Sig figs in a measurement include the known
digits plus a final estimated digit.digits plus a final estimated digit.
2.35 cm
Significant Figure Rules Count all numbers EXCEPT:Count all numbers EXCEPT:
Leading zeros -- Leading zeros -- 0.000.002525
*Decimal *Decimal present present start fromstart from left left until you until you get your first non zero numberget your first non zero number
Trailing zeros without Trailing zeros without a decimal point -- 2,5a decimal point -- 2,50000
*Decimal *Decimal absentabsent start from start from rightright until you until you get your first non zero numberget your first non zero number
4. 0.080
3. 5,280
2. 402
1. 23.50
C. Significant FiguresCounting Sig Fig Examples
1. 23.50
2. 402
3. 5,280
4. 0.080
4 sig figs
3 sig figs
3 sig figs
2 sig figs
Applying your rules
520.36 520.36 ? sig figs? sig figs 1.002501.00250 ? sig figs? sig figs 6060 ? sig figs? sig figs 458200000458200000 ? sig figs? sig figs 0.2500000.250000 ? sig figs? sig figs 0.00630000.0063000 ? sig figs? sig figs
Applying your rules
520.36 520.36 5 sig figs5 sig figs 1.002501.00250 6 sig figs6 sig figs 6060 1 sig figs1 sig figs 458200000458200000 4 sig figs4 sig figs 0.2500000.250000 6 sig figs6 sig figs 0.00630000.0063000 5 sig figs5 sig figs
Significant Figure Rules cont. Calculating with Sig FigsCalculating with Sig Figs
Multiply/DivideMultiply/Divide - The # with the - The # with the fewest sig fewest sig figs determines the # of sig figs in the answer.figs determines the # of sig figs in the answer.
(13.91g/cm3) * (23.3cm3) = 324.103g
324 g
4 SF 3 SF3 SF
Significant Figure Rules cont. Calculating with Sig Figs (con’t)Calculating with Sig Figs (con’t)
Add/SubtractAdd/Subtract – same # of digits to the rights of – same # of digits to the rights of the decimal as the measurement with the the decimal as the measurement with the smallest # smallest # of digits to the right of the decimal.of digits to the right of the decimal.
3.75 mL
+ 4.1 mL
7.85 mL
7.9 mL
3.75 mL
+ 4.1 mL
7.85 mL
Significant Figure Rules cont. Exact NumbersExact Numbers do not limit the # of sig figs in the do not limit the # of sig figs in the
answer.answer.Counting numbers: 12 studentsCounting numbers: 12 studentsExact conversions: 1 m = 100 cmExact conversions: 1 m = 100 cm““1” in any conversion: 1 in = 2.54 cm1” in any conversion: 1 in = 2.54 cm
1. (15.30 g) ÷ (6.4 mL)1. (15.30 g) ÷ (6.4 mL)
= 2.390625 g/mL
18.1 g
2. 18.9 g
- 0.84 g18.06 g
4 SF 2 SF
2.4 g/mL2 SF
Practice Problems
Rounding!RULE 1. If the first digit you remove is 4 or less, drop it and all following digits. RULE 2. If the first digit removed is 5 or greater, round up by adding 1 to the last digit kept. If a calculation has several steps, it is best to round off at the end.
Examples
Make the following into a 3 Sig Fig numberMake the following into a 3 Sig Fig number
1. 1.5587
2. .0037421
3. 1367
4. 128,522
5. 1.6683 106
1.56
.00374
1370
129,000
1.67 106
Your Final number must be of the same value as the number you started with,129,000 and not 129
Examples of RoundingFor example you want a 4 Sig Fig number
4965.03
780,582
1999.5
0 is dropped, it is <5
8 is dropped, it is >5; Note you must include the 0’s
5 is dropped it is = 5; note you need a 4 Sig Fig
4965
780,600
2000.
Scientific Notation
Converting into Sci. Notation:Converting into Sci. Notation:
Move decimal until there’s 1 digit to its Move decimal until there’s 1 digit to its left. (1-9) Places moved = exponent.left. (1-9) Places moved = exponent.
65,000 kg 6.5 × 104 kg
Only include sig figs.
Scientific Notation Rules
Large # (>1) Large # (>1) positive exponent positive exponent
(move to the left)(move to the left) Small # (<1) Small # (<1) negative exponent negative exponent
(move to the right)(move to the right) To work backwards from scientific notation To work backwards from scientific notation
to decimal notation just do the opposite.to decimal notation just do the opposite.
Scientific Notation
1. 1. 2,400,000 2,400,000 gg
2. 2. 0.00256 kg0.00256 kg
3.3. 7 7 10 10-5-5 km km
4 .4 . 6.2 6.2 10 1044 mm mm
Practice Problems
2.4 2.4 10 1066 gg
2.56 2.56 10 10-3-3 kg kg
0.00007 km0.00007 km
62,000 mm62,000 mm
Scientific Notation
Calculating with Sci. NotationCalculating with Sci. Notation(5.44 × 10(5.44 × 1077 g) ÷ (8.1 × 10 g) ÷ (8.1 × 1044 mol) = mol) =
5.44EXPEXP
EEEE÷÷
EXPEXP
EEEE ENTERENTER
EXEEXE7 8.1 4
= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol
Type on your calculator:
SI Prefix Conversions1.1. Find the difference between the exponents of the two Find the difference between the exponents of the two
prefixes.prefixes.
2.2. Move the decimal that many places.Move the decimal that many places.
3.3. Be sure to maintain sig figs!Be sure to maintain sig figs!
To the leftor right?
Copyright © 2010 Ryan P. Murphy
Copyright © 2010 Ryan P. Murphy
“I love my chocolate
Milk!”Copyright © 2010 Ryan P. Murphy
“Oh no!”
Copyright © 2010 Ryan P. Murphy
Copyright © 2010 Ryan P. Murphy
Copyright © 2010 Ryan P. Murphy
Copyright © 2010 Ryan P. Murphy
Copyright © 2010 Ryan P. Murphy
Copyright © 2010 Ryan P. Murphy
King -King - KilometerKilometer 1000m1000m 101033
Henry- Henry- HectometerHectometer 100m100m 101022
Died - Died - DecameterDecameter 10m10m 101011
By - By - Base UnitBase Unit 1m1m 101000
Drinking - Drinking - DecimeterDecimeter .1m.1m 10 10-1-1
Chocolate - Chocolate - CentimeterCentimeter .01m.01m 1010-2-2
Milk - Milk - MillimeterMillimeter .001m.001m 1010-3-3
Copyright © 2010 Ryan P. Murphy
SI Prefix Conversions
1) 20 cm = 1) 20 cm = ______________ m______________ m
2) 0.032 L = 2) 0.032 L = ______________ mL______________ mL
3) 45 3) 45 m = m = ______________ nm______________ nm
4) 805 dm = 4) 805 dm = ______________ km______________ km
0.2
0.0805
45,000
32
3
3
cm
gcm
Dimensional Analysis
The “Factor-Label” MethodThe “Factor-Label” Method Units, or “labels” are canceled, or Units, or “labels” are canceled, or
“factored” out“factored” out
g
Dimensional Analysis
Steps:Steps:
1. Identify starting & ending units.1. Identify starting & ending units.
2. Line up conversion factors so units 2. Line up conversion factors so units cancel.cancel.
3. Multiply all top numbers & divide by 3. Multiply all top numbers & divide by each bottom number.each bottom number.
4. Check units & answer.4. Check units & answer.
Dimensional Analysis
1. Taft football needs 550 cm for a 1st 1. Taft football needs 550 cm for a 1st down. How many yards is this?down. How many yards is this?
550 cm550 cm 1 in1 in
2.54 cm2.54 cm= 6.0 yd= 6.0 yd
cm yd
1 ft1 ft
12 in12 in
1 yd1 yd
3 ft3 ft
1 in = 2.54 cm1 ft = 12 in1 yd = 3 ft