Transcript 1_ Sig_ fig_ _ Rules

Counting Significant Figures:
1) All non-zero digits are significant.
– 1.5 has 2 significant figures.
2) Interior (sandwich) zeros (between two
digits) are significant.
– 1.05 has 3 significant figures.
3) Trailing zeros after a decimal point are
significant.
– 1.050 has 4 significant figures.
Tro's "Introductory Chemistry", Chapter 2
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Counting Significant Figures,
Continued
4) Leading zeros (on the left of a number) are NOT
significant.
– 0.001050 has 4 significant figures.
5) Zeros that do nothing but set the decimal point
(to the right of a number) are NOT significant:
– So 150 has 2 significant figures.
– 542,000,000 has 3 significant figures.
Tro's "Introductory Chemistry", Chapter 2
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Practice:
• How many significant figures are in each of the
following numbers?
a) 0.0035--- 2 sig. fig. (leading zeros are not significant).(Rule #4).
b) 1.080--- 4 sig. fig. (zeros after the decimal & interior zeros are
significant). (Rules #2 & 3).
c) 2371--- 4 sig. fig. (all non zeros digits are significant).(Rule #1).
d) 2.97 × 105--- 3 sig. fig. (all non zeros digits are significant)
(Rule #1).
e) 100,000--- 1 sig. fig. (zeros to the right of a # with out decimal
point are not significant) (Rule #5).
Tro's "Introductory Chemistry", Chapter 2
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Rules for rounding numbers:
1) If the digit immediate right of the last significant
figure is:
a) greater than 5 – Round up the last sig. figure:
2.536 --2.54
b) lesser than 5 – Do NOT round up:
2.532 ---2.53
c) equal to 5:
c) equal to 5:
1) followed by a non-zero –ROUND UP:
2.5351 --2.54
2) followed by zero:
If the last significant figure:
- is an odd digit – ROUND UP:
2.5350 --2.54
- is an even digit– Do NOT round up:
2.5250 ---2.52
•
•
•
•
•
Rounding to 2 significant figures:
2.34 rounds to:
2.3
2.37 rounds to:
2.4
2.349865 rounds to:
2.3
0.0234 rounds to:
0.023 or 2.3 × 10-2
0.0237 rounds to:
0.024 or 2.4 × 10-2
Tro's "Introductory Chemistry", Chapter 2
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Rounding Rules in
Addition & Subtraction:
The result must be rounded up to the same
number of digits after the decimal point than
the measurement with the fewest number of
digits after the decimal point:
28.0 cm
+ 23.538 cm
25.68 cm
77.218 cm ≈
Rounding Rules in
Addition & Subtraction:
The result must be rounded up to the same
number of digits after the decimal point than
the measurement with the fewest number of
digits after the decimal point:
28.0 cm
+ 23.538 cm
25.68 cm
77.218 cm ≈ 77.2 cm
1) 5.74 +
Practice:
0.823 + 2.651 = 9.214 = 9.21
2 decimal 3 decimal 3 decimal
places
places
places
2) 4.8
-
1 decimal
place
3.965
= 0.835
= 0.8
3 decimal
places
Tro's "Introductory Chemistry", Chapter 2
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Rounding Rules in Multiplication &
Division:
The answer must have the same number of
significant figures as the measurement with
the fewest number of significant figures:
24 x 3.28 = 78.72 ≈ 79
23.5 x 1.2 = 28.2 ≈ 28
60.2 ÷ 20.1 = 2.995 ≈ 3.00
Practice:
1) 5.02 ×
3 sig. figs.
89.665 × 0.10 = 45.0118 = 45
5 sig. figs.
2) 5.892 ÷ 6.10
4 sig. figs.
2 sig. figs.
= 0.96590 = 0.966
3 sig. figs.
3) 1.01 × 0.12 × 53.51 ÷ 96 = 0.06775 = 0.068
3 sig. figs. 2 sig. figs. 4 sig. figs. 2 sig. figs.
4) 56.55 × 0.920 ÷ 34.2585 = 1.51863 = 1.52
4 sig. figs.
3 sig. figs.
6 sig. figs.
Tro's "Introductory Chemistry", Chapter 2
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