The answers here are presented in bold.


Some notes:

  1. Ordinary Number and Appropriate form are subjective. For example capacitance (farad, F) is more often written in pF, or µF, even when other prefixes could be used. For example, 4700 µF is used more often than 4.7 mF, and capacitances between 1 nF and 1 µF are often given in pF or µF e.g. 0.047 µF instead of 47 nF, or 1200 pF (or 0.0012 µF) instead of 1.2 nF.

  2. Normally, the exponent in Engineering Notation is never greater than the exponent in Scientific Notation.

  3. The mantissa (or significand) of a Scientific Notation or the significand of an Engineering Notation number is normally at least 1.


Question 1

Convert the following to the given multiple or sub-multiple.

The comment column shows what you multiply the existing submultiple quantity by to get the desired submultiple quantity.

Existing
Submultiple
Quantity
 Desired
Submultiple
Quantity
 Comment
50,000 Ω 50 kΩ 1 Ω = 0.001 kΩ. Example, already filled in.
2,345 V 2.345 kV 1 V = 0.001 kV
500,000,000 Ω 500 MΩ 1 Ω = 10-6 MΩ
4,500 A 4.5 kA
 1 A = 0.001 kA
12,340,000,000,000 Wh 12.34 TWh 1 Wh = 10-12 TWh
270,000 W 0.27 MW 1 W = 0.000001 W
25,450 V 25.45 kV 1 V = 0.001 kV
265.5 A 0.2655 kA 1 A = 0.001 kA
0.000 023 4 J 23.4 µJ 1 J = 1000000 µJ
0.000 05 A 50 µA 1 A = 1000000 µA. Example, already filled in.
0.002 5 A 2.5 mA 1 A = 1000 mA
0.002 W 2 mW 1 W = 1000 mW
2 W
2000 mW
1 W = 1000 mW
0.000 14 Ω 140 µΩ 1 Ω = 1000000 µΩ
0.056 V 56 mV 1 V = 1000 mV
0.000 000 000 04 F 40 pF 1 F = 1012 pF. This one is more complicated, as most 10-digit calculators cannot accept a number with this many leading zeros. Instead, a digit counting approach is more appropriate.

To get picofarads (pF), the decimal point has to be moved 12 places to the right, to get 040 (a trailing zero needs to be added after the 4 to make '04' a three-digit group).
0.000 000 000 04 F 0.04 nF 1 F = 109 nF. This one is more complicated, as most 10-digit calculators cannot accept a number with this many leading zeros. Instead, a digit counting approach is more appropriate.

To get nanofarads (nF), the decimal point has to be moved nine places to the right, to get '0.04'. The decimal point is shifted so that 0.000 000 000 04 becomes '0.04'. While this notation might be considered unusual, the notation to use is situation-dependent.
45,000 V 45 kV 1 V = 0.001 kV


Question 2

Convert the following to base units.

Other than the type of target unit, Question 2 is similar to Question 1.

NOTE: These units (except 'A', amps) are not 'base units' in the manner defined by the SI. A better way of thinking of this question is "convert these quantities to units without prefixes".

Existing
Quantity
 Desired
Prefix-Less
Quantity
 Comment
20 MΩ 20,000,000 Ω 1 MΩ = 1000000 Ω. Example, already filled in.
1500 kV 1,500,000 V 1 kV = 1000 V
50 kA 50,000 A 1 kA = 1000 A
1.6 kV 1600 V
 1 kV = 1000 V
0.56 MΩ 560,000 Ω 1 MΩ = 1000000 Ω
0.2 kV 200 V 1 kV = 1000 V
0.000 5 GW 500000 W 1 GW = 109 W. Don't be put off by the quantity being less than 1. Multiplying 0.0005 by 109 will still yield the correct answer. Conversely, this quantity can also be thought of as 0.5 MW, or 500 kW.
0.000 005 TWh 5000000 Wh 1 TWh = 1012 Wh. Don't be put off by the quantity being less than 1. Multiplying 0.000005 by 1012 will still yield the correct answer. Conversely, this quantity can also be thought of as 0.005 GWh, or 5 MWh.
0.016 kV 16 V 1 kV = 1000 V
200 mA 0.2 A 1 mA = 0.001 A. Example, already filled in.
1200 mA 1.2 A 1 mA = 0.001 A
0.54 mA 0.00054 A 1 mA = 0.001 A. This quantity may also be expressed in Scientific Notation as 5.4 × 10-4 A, which may help with determining the answer.
12.6 mH 0.0126 H 1 mH = 0.001 H
500,000 nF 0.0005 F 1 nF = 10-9 F. The calculation may be thought of as 500000 × 10-9 F = 5 × 105 × 10-9 F = 5 × 105-9 F = 5 × 10-4 F = 0.0005 F.
50 µF 0.00005 F 1 F = 1012 pF. The calculation may be thought of as 50 × 10-6 F = 5 × 10-5 F = 0.00005 F.
85,000 mA 85 A 1 mA = 0.001 A
85,000,000,000 pH 0.085 H 1 pH = 10-12 H. The calculation may be thought of as 85000000000 × 10-12 H = 85 × 109 × 10-12 H = 85 × 109-12 H = 85 × 10-3 H = 0.085 H.
25.64 µH 0.00002564 H 1 µH = 10-6 H.


Question 3

Convert to the given multiple or sub-multiple.

To ease this question, I will create a conversion table between the prefixes.

For example, to convert 20 µg to kg, look up the 'µ' row. The conversion factor for 'k' (the 'k' column) is 10-9. In other words, to convert µg to kg, you need to multiply the µg quantity by 10-9. So 10 µg = 20 × 10-9 = 2 × 10-8 = 0.00000002 kg.

p n µ m - k M G T
p 1
 10-3
 10-6
 10-9
 10-12
 10-15
 10-18
 10-21
 10-24
n 103 1 10-3
 10-6
 10-9
 10-12
 10-15
 10-18
 10-21
µ 106 103 1 10-3
 10-6
 10-9
 10-12
 10-15
 10-18
m 109 106 103 1 10-3
 10-6
 10-9
 10-12
 10-15
- 1012 109 106 103 1 10-3
 10-6
 10-9
 10-12
k 1015
 1012 109 106 103 1 10-3
 10-6
 10-9
M 1018
 1015
 1012 109 106 103 1 10-3
 10-6
G 1021
 1018
 1015
 1012 109 106 103 1 10-3
T 1024
 1021
 1018
 1015
 1012 109 106 103 1


Make sure you memorise the patterns in the table.

It is also possible to eliminate the prefix, then add it again. For example, converting 85,000,000,000 pH to mH. 85,000,000,000 pH = 85 × 10-3 H. 1 H = 1000 mH, so 85,000,000,000 pH = 85 × 10-3 × 1000 mH = 85 mH.

Existing
Quantity
 Desired
Quantity
 Comment
20,000 mΩ 0.020 kΩ 1 mΩ = 10-6 kΩ. Example, already filled in.
345 kV 0.345 MV 1 kV = 0.001 MV
0.789 mH 789 µH 1 mH = 1000 µH
57,000,000 mV 57 kV
 1 mV = 10-6 kV
107 pF 0.107 nF 1 pF = 0.001 nF
0.000 05 kV 50 mV 1 kV = 106 mV
250 nF 250,000 pF 1 nF = 1000 nF. Example, already filled in.
60,000 kΩ 60 MΩ 1 kΩ = 0.001 MΩ
0.045 µF 0.000045 mF 1 µF = 0.001 mF
65,000 kΩ 65,000,000,000 mΩ 1 kΩ = 106 mΩ. Note the output is in milliohms.
0.079 nF 0.000000079 mF 1 nF = 10-6 mF. The calculation may be thought of as 0.079 × 10-9 F = 0.079 × 10-6 × 10-3 F = 0.079 × 10-6 mF = 0.000000079 mF.
0.026 nA 26 pA 1 pA = 1000 nA



آخر تعديل: الجمعة، 15 مايو 2020، 1:31 PM