Practice Problem (KEY)#
Convert the following numbers to engineering notation:
46500000 V → 46.5 MV
0.00000983 A → 9.83 µA
792000000000 Ω → 792 GΩ
6150 V → 6.15 kV
0.0019 A → 1.9 mA
20000000000 Ω → 20 GΩ
Use the decision matrix below to determine which laptop would be the best choice.
Screen Size
Cost
Laptop A
15
$1000
Laptop B
17
$1200
Decision matrix (assume larger screen size is desired):
Laptop
Screen Size
Cost
Total
Weight
Value
Norm
Weighted
Value
Norm
Weighted
A
15
0.882
1000
1.000
B
17
1.000
1200
0.833
Determine which house would be the best choice.
Commute Time
Square Footage
Cost
House A
15 min
2000
$220000
House B
5 min
1500
$250000
House C
30 min
3000
$200000
Decision matrix (shorter commute time, larger square footage, and lower cost are desired):
House
Commute Time
Square Footage
Cost
Total
Weight
Determined in Class
Determined in Class
Determined in Class
Value
Norm
Weighted
Value
Norm
Weighted
Value
Norm
Weighted
A
15
0.333
2000
0.667
$220K
0.909
B
5
1.000
1500
0.500
$250K
0.800
C
30
0.167
3000
1.000
$200K
1.000
You are evaluating three different AC-to-DC converters that all meet your requirements for ripple and cost. Since you want to use these devices for a scientific instrument, you really want to minimize ripple but are limited by a small budget. Use a decision matrix to choose the best one. Assume a weight of 60% for ripple and 40% for cost.
Part
Ripple
Cost
A
30 mV
$20
B
35 mV
$14
C
45 mV
$12
Part
Ripple
Cost
Total
Weight
0.6
0.4
Value
Norm
Weighted
Value
Norm
Weighted
A
30 mV
1.000
0.600
$20
0.600
0.240
0.840
B
35 mV
0.857
0.514
$14
0.857
0.343
0.857
C
45 mV
0.667
0.400
$12
1.000
0.400
0.800
Part B is the best AC-to-DC converter because it has the highest total score.
Three options are proposed to provide power to a new community. The cost and efficiency for each option are shown below.
Option
Cost
Efficiency
X
$3.2M
99.4%
Y
$3.0M
97.2%
Z
$2.8M
86.0%
(a) If cost and efficiency are considered equally as important, which is the better option?
Option
Cost
Efficiency
Total
Weight
0.5
0.5
Value
Norm
Weighted
Value
Norm
Weighted
X
$3.2M
0.875
0.438
99.4%
1.000
0.500
0.938
Y
$3.0M
0.993
0.467
97.2%
0.978
0.489
0.956
Z
$2.8M
1.000
0.500
86.0%
0.865
0.433
0.933
Part Y is the best option because it has the highest total score.
(b) If efficiency is considered 9 times as important as cost, which is the better option?
\[Weight_{cost} + Weight_{efficiency} = 1\]\[Weight_{efficiency} = 9 \cdot Weight_{cost}\]\[Weight_{cost} + 9 \cdot Weight_{cost} = 1\]\[Weight_{cost} = \frac{1}{10} = 0.1\]\[Weight_{efficiency} = \frac{9}{10} = 0.9\]Option
Cost
Efficiency
Total
Weight
0.1
0.9
Value
Norm
Weighted
Value
Norm
Weighted
X
$3.2M
0.875
0.088
99.4%
1.000
0.900
0.988
Y
$3.0M
0.993
0.093
97.2%
0.978
0.880
0.973
Z
$2.8M
1.000
0.100
86.0%
0.865
0.779
0.879
Part X is the best option because it has the highest total score.
Convert the following into engineering notation:
(a) 5.45 × 10^-7 A → 545 nA
(b) 123,400 W → 123 kW
(c) 8.33 × 10^7 V → 83.3 MV
(d) 4.3 × 10^10 bits → 43 Gb
(e) 1,497,000 Hz → 1.497 MHz
(f) 76.2 × 10^-4 m → 7.62 mm
(g) 2.31 × 10^-5 m → 23.1 µm
(h) 1.78 × 10^-14 W → 17.8 fW