C. What are Significant Figures The places in the numbers that are The places in the numbers that are important. They tell you how precise a important. They tell you how precise a measurement is. measurement is. Recording Sig Figs Recording Sig Figs Sig figs in a measurement include Sig figs in a measurement include the known digits plus a final the known digits plus a final estimated digit estimated digit 2.35 cm
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C. What are Significant Figures The places in the numbers that are important. They tell you how precise a measurement is. The places in the numbers that.
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C. What are Significant Figures The places in the numbers that are important. The places in the numbers that are important.
They tell you how precise a measurement is.They tell you how precise a 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 digitdigits plus a final estimated digit
2.35 cm
C. Significant Figures 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
C. Significant Figures 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
C. Significant Figures 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
224 g
+ 130 g
354 g 7.9 mL 350 g
3.75 mL
+ 4.1 mL
7.85 mL
224 g
+ 130 g
354 g
C. Significant Figures 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
C. Significant Figures
5. (15.30 g) ÷ (6.4 mL)5. (15.30 g) ÷ (6.4 mL)
Practice Problems
= 2.390625 g/mL
18.1 g
6. 18.9 g
- 0.84 g18.06 g
4 SF 2 SF
2.4 g/mL2 SF
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.
Chapter Two10
Practice Rule #2 Rounding
Make the following into a 3 Sig Fig numberMake the following into a 3 Sig Fig number
1.5587
.0037421
1367
128,522
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.
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.