Measuring. What are Significant Figures Any digit of a number that is known with certainty. They tell you how precise a measurement is. Any digit of a.

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