1. Chapter 2 Measurements 2.3 Measured Numbers and Significant Figures
Learning Goal Identify a number as measured or exact; determine the number of significant figures in a measured number.
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2. provides numbers for a measurement called measured numbers
A measuring tool
is used to determine a quantity such as the length or the mass of an object
provides numbers for a measurement called measured numbers
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3. To report the length of an object
Reporting Length
To report the length of an object
observe the numerical values of the marked lines at the end of the object
estimate the last digit by visually dividing the space between the smallest marked lines
This estimated number is the final digit that is reported for a measured number.
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4. The end of the object is between the 4-cm and 5-cm marks.
Reporting Length – 4.5 cm
The end of the object is between the 4-cm and 5-cm marks.
Estimate that the end is halfway between the 4-cm and 5-cm marks and report the value as 4.5 cm.
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5. The metric ruler is marked at every 0.1 cm.
Reporting Length – 4.55 cm
The metric ruler is marked at every 0.1 cm.
You can now estimate that the length is halfway between the 4.5-cm and 4.6-cm marks and report the value as 4.55 cm.
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6. The end of the object lines up with the 3-cm mark.
Reporting Length – 3.0 cm
The end of the object lines up with the 3-cm mark.
Because the divisions are marked in units of 1 cm, the estimated digit appears in the tenths place (0.1 cm).
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7. What is the length of the red line? (1) 9.0 cm (2) 9.03 cm (3) 9.04 cm
Learning Check
. l l l l l cm
What is the length of the red line?
(1) cm
(2) cm
(3) cm
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8. The length of the line could be reported as (2) 9.03 cm (3) 9.04 cm
Solution
. l l l l l cm
The length of the line could be reported as
(2) cm
(3) cm
The estimated digit may be slightly different. Both readings are acceptable.
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9. All nonzero numbers are counted as significant figures.
In a measured number, the significant figures, (SFs) are all the digits, including the estimated digit.
All nonzero numbers are counted as significant figures.
Zeros may or may or may not be significant, depending on the position in the number.
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10. Rules for Significant Figures
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11. Counting Significant Figures
All nonzero numbers in a measured number are significant.
Measurement Number of
Significant Figures
38.15 cm
5.6 ft
65.6 lb m
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12. Zeros between nonzero digits are significant. Measurement Number of
Zeros Between Digits
Zeros between nonzero digits are significant.
Measurement Number of
Significant Figures
50.8 mm
2001 min lb m
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13. Zeros at the end of decimal numbers are significant.
Zeros, Decimal Numbers
Zeros at the end of decimal numbers are significant.
Measurement Number of
Significant Figures
50.80 km
200. min
40.00 g
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14. Zeros at the beginning of decimal numbers are not significant.
Zeros, Decimal Numbers
Zeros at the beginning of decimal numbers are not significant.
Measurement Number of
Significant Figures
0.440 km
0.022 g lb
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15. Zeros, Nondecimal Numbers
Zeros at the end of nondecimal numbers are not significant.
Measurement Number of
Significant Figures km
810 cm g
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16. Zeros, Scientific Notation
Zeros in the coefficient of numbers written in scientific notation are significant.
Measurement Number of
Significant Figures
4.90 × 103 m
8.0 × 10–3 kg
× 10–5 L 5
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17. Zeros, Scientific Notation
Keep only the significant zeros when writing numbers in scientific notation.
Measurement Scientific Number of
Notation Significant
Figures
500. g × 102 g 3
m × 105 m 1
0.300 cm × 10−1 cm 3
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18. those numbers obtained by counting items
Exact Numbers
Exact numbers are
those numbers obtained by counting items
definitions that compare two units in the same measuring system
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19. Exact Numbers
Exact numbers are not measured, do not have a limited number of significant figures, and do not affect the number of significant figures in a calculation.
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20. Learning Check
State the number of significant figures in each of the following measurements:
A m
B L
C g
D m
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21. Solution
State the number of significant figures in each of the following measurements:
A m 2 SF
B L 4 SF
C g SF
D m 3 SF
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22. A. Which answer contains three significant figures?
Learning Check
A. Which answer contains three significant figures?
(1) (2) (3) × 103
B. All the zeros are significant in
(1) (2) (3) × 103
C. The number of significant figures in × 102 is
(1) one (2) two (3) three
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23. A. Which answer contains three significant figures? (2) 0.00476
Solution
A. Which answer contains three significant figures?
(2)
B. All the zeros are significant in
(2) (3) ×103
C. The number of significant figures in × 102 is
(3) three
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