The prefix "milli" means "one thousandth". To convert from amperes (A) to milliamperes (mA), multiply by 1,000 (move the decimal point three places to the right).

\[1.5 \times 1{,}000 = 1{,}500\]

So 1.5 amperes equals 1,500 milliamperes.

Memory aids:

• Move the decimal point three places to the right to go from amperes to milliamperes (multiply by 1,000).
• A quick check: to convert milliamps to amps, change the comma (thousands separator) to a decimal point. For example, \(1{,}500 mA = 1.500 A\).

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Convert hertz to kilohertz by remembering that 1 kHz = 1,000 Hz. Dividing the given frequency by 1,000 gives the value in kilohertz:

1,500,000 Hz ÷ 1,000 = 1,500 kHz

You can also express the frequency in megahertz: 1,500,000 Hz ÷ 1,000,000 = 1.5 MHz. A common mistake is to read 1,500,000 Hz as 1,500 MHz, but 1,500 MHz would be 1,500,000,000 Hz (one thousand times larger).

Memory aids:

• kilo (k) = 1,000; move the decimal 3 places left to go from Hz to kHz
• mega (M) = 1,000,000; move the decimal 6 places left to go from Hz to MHz
• To go from Hz to kHz divide by 1,000; to go to MHz divide by 1,000,000

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The prefix "kilo" (used in metric units) means "thousand." Therefore, a kilovolt is equal to one thousand volts.

Memory aids:

• kilo = 10^3 = 1,000
• Examples: 1 kilometer = 1,000 meters; 1 kilogram = 1,000 grams
• Reference: http://en.wikipedia.org/wiki/Kilo-

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micro is a prefix in the metric system meaning "one-millionth". Thus, a microvolt is one millionth (1/1,000,000) of a volt. One microvolt is written as 1μV.

One one-thousandth of a volt is denoted with the milli prefix (a millivolt). One millivolt is written as 1mV.

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1000 milliwatts (mW) = 1 watt (W). Therefore 500 milliwatts = 500 / 1000 = 0.5 watts.

Memory aids:

• The prefix "milli-" means one thousandth, so 1000 milliwatts = 1 watt.
• Think in terms of dividing by 1000 to convert milliwatts to watts.

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A milliampere (mA) is one thousandth of an ampere (A). To convert milliamperes to amperes, divide by 1000.

3000 milliamperes ÷ 1000 = 3 amperes.

Therefore, 3000 mA equals 3 A.

Memory aids:

• "milli" means 1/1000 (10⁻³).
• 1000 mA = 1 A, so 3000 mA = 3 A.
• To convert mA to A, move the decimal point three places to the left.

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1 MHz equals 1,000 kHz, so to convert megahertz to kilohertz multiply by 1,000.

Using the value given: 3.525 MHz × 1,000 = 3525 kHz.

You can show the unit cancellation explicitly:

\(\frac{3.525\text{ MHz} \times 1000 \text{ kHz}}{1 \text{ MHz}} = 3525 \text{ kHz}\)

Because the fraction \(\frac{1000 \text{ kHz}}{1 \text{ MHz}}\) equals 1, the numeric value is unchanged except for the unit conversion.

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Convert between metric prefixes for capacitance.

Working stepwise:

\[ \begin{align} 1 \mu F &= 1{,}000 nF\\ 1 nF &= 1{,}000 pF\\ \end{align} \]

So:

\[ \begin{align} 1 \mu F &= 1{,}000 nF\\ &= 1{,}000 \times 1{,}000 pF\\ &= 1{,}000{,}000 pF\\ \end{align} \]

Or, written the other direction:

\[ \begin{align} 1{,}000{,}000 pF &= 1{,}000 nF\\ &= 1 \mu F\\ \end{align} \]

Using decimals:

\[ \begin{align} 1{,}000{,}000 pF &= 1{,}000{,}000 \times 10^{-12} F\\ &= 10^6 \times 10^{-12} F\\ &= 10^{-6} F\\ &= 1 \mu F\\ \end{align} \]

Using exponents:

\[ \begin{align} 10^6 pF &= 10^6 \times 10^{-12} F\\ &= 10^{6-12} F\\ &= 10^{-6} F\\ &= 1 \mu F\\ \end{align} \]

Therefore:

\[ 1{,}000{,}000 pF = 1 \mu F \]

Memory aids:

• Every step between common metric prefixes changes by a factor of \(1{,}000\).
• The common capacitance prefixes go:

\[ \begin{align} milli &\rightarrow micro \rightarrow nano \rightarrow pico\\ 10^{-3} &\rightarrow 10^{-6} \rightarrow 10^{-9} \rightarrow 10^{-12}\\ \end{align} \]

• Each step moves three decimal places.
• A simple prefix sheet with three zeros under each prefix makes it easy to read:

\[ \begin{align} 1 \mu F &= 1{,}000 nF\\ &= 1{,}000{,}000 pF\\ \end{align} \]

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Doubling power corresponds to an increase of about \(3 dB\). Going from \(5 watts\) to \(10 watts\) is exactly a doubling of power, so the change is approximately \(+3 dB\).

You can also use the decibel formula for power:

\[ dB = 10 \times \log_{10}\left(\frac{P_1}{P_0}\right) \]

For this case:

\[ \begin{align} dB &= 10 \times \log_{10}\left(\frac{10}{5}\right)\\ &= 10 \times \log_{10}(2)\\ &\approx 3.01 dB\\ &\approx 3 dB \end{align} \]

As a check, four times the power is about \(6 dB\) because it is two doublings:

\[ \begin{align} 2 \times 2 &= 4\\ 3 dB + 3 dB &= 6 dB \end{align} \]

Halving the power is about \(-3 dB\).

Memory aids:

• \(+3 dB \approx\) double the power
• \(-3 dB \approx\) half the power
• \(+6 dB \approx\) four times the power, or two doublings
• Use \(dB = 10 \times \log_{10}\left(\frac{P_1}{P_0}\right)\) for exact calculations

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Decibels measure power ratios on a logarithmic scale. A change of \(+3 dB\) corresponds to a doubling of power, and a change of \(-3 dB\) corresponds to halving the power.

Going from \(12 watts\) to \(3 watts\) is a reduction to one quarter of the original power:

\[ \begin{align} 3 &= \frac{12}{4}\\ \frac{3}{12} &= \frac{1}{4} \end{align} \]

One quarter is two successive halvings, so the total change is:

\[ \begin{align} -3 dB + -3 dB &= -6 dB \end{align} \]

You can also use the formula for power level change in decibels:

\[ dB = 10 \times \log_{10}\left(\frac{P_{new}}{P_{old}}\right) \]

For this case:

\[ \begin{align} dB &= 10 \times \log_{10}\left(\frac{3}{12}\right)\\ &= 10 \times \log_{10}\left(\frac{1}{4}\right)\\ &\approx 10 \times (-0.60206)\\ &\approx -6.02 dB\\ &\approx -6 dB \end{align} \]

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The decibel change for a power ratio is given by the formula:

\[ L_{dB} = 10 \times \log_{10}\left(\frac{P_1}{P_0}\right) \]

Here \(P_1\) is the new power, \(200 W\), and \(P_0\) is the original power, \(20 W\).

So:

\[ \begin{align} L_{dB} &= 10 \times \log_{10}\left(\frac{200}{20}\right)\\ &= 10 \times \log_{10}(10)\\ &= 10 \times 1\\ &= 10 dB \end{align} \]

Thus the power increase from \(20 watts\) to \(200 watts\) corresponds to a \(10 dB\) increase.

Memory aids:

• \(10 dB\) corresponds to a \(10\times\) change in power.
• Every \(+3 dB\) approximately doubles the power, and every \(-3 dB\) approximately halves it.
• Example doubling steps from \(20 W\):

\[ \begin{align} +3 dB &\rightarrow 40 W\\ +6 dB &\rightarrow 80 W\\ +9 dB &\rightarrow 160 W\\ +12 dB &\rightarrow 320 W \end{align} \]

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To convert kilohertz (kHz) to megahertz (MHz), move the decimal point three places to the left (because \(1 MHz = 1000 kHz\)).

With \(28,400 kHz\) the decimal point is assumed to be at the end: 28400. Moving that decimal three places left puts it between the \(28\) and the \(400\), giving 28.400

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One gigahertz (GHz) equals 1000 megahertz (MHz). Converting MHz to GHz means dividing by 1000.

Dividing 2425 MHz by 1000 gives \(\frac{2425}{1000} = 2.425 GHz\), so the frequency is 2.425 GHz.

Memory aids:

• Move the decimal point three places to the left to convert MHz to GHz.
• Remember 1 GHz = 1000 MHz.

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