1. Units of Measurement
(1.3) & (1.4) Systems of Units

2. Table 1.1 (p. 9) English, Metric, & SI Units
English – inch, mile, pound, ounce
Metric – base-10, CGS and MKS
CGS – Based on centimeter, gram, second
MKS – Based on meter, kilogram, second
SI – International System, modern metric

3. Problem 6 (p. 29)
A pitcher has the ability to throw a baseball at 95 mph. What is the speed in ft/s? ft s ? ft s
95 mi h
5280 ft mi
1 h _
60 min
1 min
60 s = * * *

4. Problem 6 (p. 29) part b
How long does the hitter have to make a decision about swinging at the ball if the plate and the mound are separated by 60 feet?
v = d t
t = d v
60 ft _
ft/s
= ?
= s

5. Problem 6 (p. 29) part c.
If the batter wanted a full second to make a decision, what would the speed in mph have to be? d t
60 ft
1 s
60 s_
1 min
60 min
1 h
1 mi_
5280 ft ?
v = = * * * =
= mph

6. 1.5 Significant figures, accuracy, and rounding off
1.2 V and 1.20 V
Imply different levels of accuracy

7. Accuracy and Precision
Accuracy = freedom from error (exactness)
Precision = The degree of refinement with which an operation is performed or a measure stated
The precision of a reading can be determined by the number of significant figures (digits) present.

8. When adding a quantity accurate only to the tenths place to a number accurate to the thousandths place will result in a total having accuracy only to the tenths place. In the addition or subtraction of approximate numbers, the entry with the lowest level of accuracy determines the format of the solution.

9. Example 1.1 (p. 12) 532.6 ≈ 536.7 4.02 (as determined by
≈ 536.7
(as determined by ) =

10. Example 1.1 (p. 12)
b ≈ (as determined by 0.04) =

11. 1.6 Powers of Ten _ 1 _ _ 1 _ 1000 10 = = 10 __ 1 __ _ 1 _ 0.00001 10-3
= 10 3
__ 1 __ _ 1 _ 5 =
= 10 -5

12. Addition and Subtraction
A * 10 ± B * 10 = (A ± B) * 10 Example: = (6.3 * 10 ) + (75 * 10 ) = ( ) * 10 = 81.3 * 10 3 3 3 3

13. Multiplication n m
n + m
(a* 10 ) (B * 10 ) = (A)(B) * 10 Example: (0.0002) ( ) = (2) * 10 * (7) * 10 = 14 * 10 -4 -6
-10

14. Division A * 10_ A B * 10 B = * 10 Example: 0.00047 0.002 47 * 10_
n-m =
* 10 m
Example: -5
0.002
47 * 10_
2 * 10 -2
= 23.5 * 10 = -3

15. ( ) Powers = 125 * 10 (A * 10 ) = A * 10 Example: __1___ 0.0005 =n m nm
Example: ( )
__1___
0.0005 3 3 -5 3
-15 =
(5 * 10 ) = 5 * 10
-15
= 125 * 10

16. 1.7: Fixed-Point, Floating Point, Scientific, and Engineering Notation
* Fixed Point – Choose the level of accuracy for the output – example: tenths, hundredths or thousandths place 1 3 1 16
= 0.333
= 0.063
2300 2 =

17. Floating Point Number of significant figures varies 1 3
= … 1 16 =
2300 2
= 1150

18. Scientific Notation
Scientific notation requires that the decimal point appear directly after the first digit greater than or equal to 1, but let than 10. 1 3
= E-1 1 16
= 6.25 E-2
2300 2
= 1.15 E3

19. Engineering Notation
Engineering notation specifies that all powers of ten must be multiples of 3, and the mantissa must be greater than or equal to 1 but less than 1000 1 3
= E-3 1 16
= 62.5 E-3
2300 2
= 1.15 E3

20. Engineering Notation and Accuracy
Using engineering notation with two-place accuracy will result in: 1 3
= E-3 1 16
= E-3
2300 2
= 1.15 E3

21. Look at table 1-2 for prefixes

22. 1.8 Conversion Between Levels of Powers of Ten
20 kHz = ______________ MHz
20 * 10_ Hz 3 -6 -3
* = * 10
= 0.02 MHz

23. Conversion: Continued
0.04 ms = ___________ μs -2
4 * 10_ s +1 -3 6
* 10 * = * 10 μs
or 40 μs

24. ( ) ( ) 1.9 Conversion 0.5 day = _____ min 0.5 day 24 h 60 min

25. Determine the speed in miles per hour of a competitor who can run a 4-min mile.( ) ( )
1 mi 4 min
60 min
1 h
60 mi
4 hr
15 mi h = =
15 mph

26. Rate = 14.4 kbps, Capacity = 1.44 MB 1.44 MB = 1.44 * 2 * 8 bit
Data is being collected automatically from an experiment at a rate of 14.4 kbps. How long will it take to completely fill a diskette whose capacity is 1.44 MB?
Rate = 14.4 kbps, Capacity = 1.44 MB 20
1.44 MB = 1.44 * * 8 bit
Capacity
Rate
Capacity
Time
so Time =
Rate =
bytes 20
bits
(1.44 MB) ( ) (8 _)
(14.4 * )(60 ) MB
byte
= min
t =
bits 3
sec
sec
min

27. Number Systems (N) = [(integer part) . (fractional part)]
Radix point
(N) = [(integer part) . (fractional part)] n
Two common number representations
Juxtapositional – placing digit side-by-side
Non-juxtapositional

28. Juxtapositional (N) = (a a … a a a a … a )
Radix point
(N) = (a a … a a a a … a ) n
n-1
n-2 1 0. -1
n-2 -m
R = Radix of the number system
n = number of digits in the integer portion
m = number of digits in the fractional portion
a = MSD
n-1
a = LSD -m

29. Base Conversion
= ( ) 10 2
1 _
1010
1 _
1010
1 _
1010
[(0001 * 1010) + (1001 * 0001) + (0111 * ) * ]
2 ___ 1
2___1
2___0 19 9 4 2 1
10011
0.75 2
1.50
1.00
______x = 1
______x 1
.11