SIGNIFICANT FIGURES AMOLE 2015. WHAT & WHY? Refer to them as “Sig Figs” for short Used to...
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Transcript of SIGNIFICANT FIGURES AMOLE 2015. WHAT & WHY? Refer to them as “Sig Figs” for short Used to...
WHAT & WHY?
Refer to them as “Sig Figs” for short Used to communicate the degree of
precision measured Example - Scientists records: 50 mL
Does that mean… 50 mL exact?Could he only measure to the ones place?
Did he round up from 49.8?Is it really 50.12 mL?
RULE #1: NON ZEROS Every nonzero digit is
significant. If it’s not a zero, it will count Examples:
24 = 2 sig figs 3.56 = 3 sig figs 7 = 1 sig figs
COUNT!
RULE #2: CAPTURED ZEROS
Also called “trapped” or “sandwiched” zeros
Zeros between non-zeros are significant
Examples: 7003 = 4 sig figs 40.9 = 3 sig figs 60.09 = ?
COUNT!
RULE #3: LEADING ZEROS Zeros appearing in front of non-
zero digits are not significantAct as placeholdersCan’t be dropped, show magnitude
Examples: 0.00024 = 2 sig figs 0.453 = 3 sig figs 0.003 = ?
DON’T COUNT
RULE #4: TRAILING ZEROS Zeros at the end of a number with a decimal point are significant.
At the end and to the right of a decimal point
Examples: 43.00 = 4 sig figs 1.010 = 4 sig figs 1.50 = ?COUNT!
RULE #5: TRAILING ZEROS Zeros at the end of a number without a decimal point are not significant.
At the end and to the right of a decimal point
Examples: 300 = 1 sig figs 27,300 = 3 sig figs 120 = ?DON’T COUNT
All non-zero digits DO count. Leading zeros DON’T count.
(zeros in front of numbers)
Captive Zeros DO count.(zeros between non-zero numbers)
Trailing Zeros DO count IF the number contains a DECIMAL.(zeros at the end of numbers)
TRY THESE!
4.012
87,900
91.0005
500,001
0.005
0.6010
7,040, 100
2.100
= 4 sig. figs.= 3 sig. figs.= 6 sig. figs.= 6 sig. figs.= 1 sig. figs.= 4 sig. figs.= 5 sig. figs.= 4 sig. figs.
ADDING & SUBTRACTING The answer cannot be more precise than
the values in the calculation The answer is rounded off so it contains
the same decimal places as the number in the problem with the fewest .
Example: 12.11 + 18.0 = 30.1112.11 = 2 decimal places18.0 = 1 decimal place
12.11 + 18.0 = 30.1
YOU TRY: 2.140 + 0.023 = ?
2.140 = 3 decimal places0.023 = 3 decimal places
Answer unrounded: 2.163 Answer with appropriate sig figs:
2.163
MULTIPLYING & DIVIDING The answer cannot be more precise than
the values in the calculation Answer should contain the same number
of sig figs as the number with the least sig figs in the problem: Example: 4.56 x 1.4 = 6.38
4.56 = 31.4 = 2
4.56 x 1.4 = 6.4
YOU TRY:1.20 x 0.51 = ?
1.20 = 30.51 = 2
Answer unrounded: 0.612
Answer with appropriate sig figs: 0.61
TRY THESE!
4.01 + 0.03
87.957 – 85.1
4.13 x 1.2
500 / 5.5
= 4.04 = 4.04
= 2.857 = 2.9
= 4.956 = 5.0
= 90.90909 = 90