Converting Electrical Quantities Across SI Units

Kia ora. Last lesson established the calculation habit that comes before choosing a formula: record the known values with their units, identify the requested quantity, and flag any units that may need conversion.

This lesson develops that last step. Electrical questions regularly mix units such as $\text{mA}$, $\text{A}$, $\text{k}\Omega$, $\text{M}\Omega$, $\text{kW}$, and $\mu \text{F}$. A prefix conversion does not change the physical quantity; it only changes how the same quantity is written. By the end, you should be able to convert confidently and show a clear, exam-mark-friendly calculation line.

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Prefixes are powers of ten

A prefix tells you how large or small a unit is compared with its unprefixed form. For electrical calculations, think of $\text{A}$, $\Omega$, $\text{W}$, $\text{F}$, $\text{H}$, and $\text{Hz}$ as the no-prefix forms.

For example:

$$1\text{k}\Omega =1000\Omega$$ $$1\text{mA}=0.001\text{A}$$

So a kilohm is a larger unit than an ohm, while a milliamp is a smaller unit than an ampere.

The most useful prefixes for pre-trade electrical work are below.

Prefix	Symbol	Meaning	Power of ten	Typical electrical use
giga	$\text{G}$	billion times	$10^9$	$\text{GHz}$
mega	$\text{M}$	million times	$10^6$	$\text{M}\Omega$, $\text{MW}$
kilo	$\text{k}$	thousand times	$10^3$	$\text{k}\Omega$, $\text{kW}$, $\text{kHz}$
no prefix	none	one unit	$10^0$	$\text{A}$, $\Omega$, $\text{W}$, $\text{F}$
milli	$\text{m}$	one thousandth	$10^{-3}$	$\text{mA}$, $\text{mV}$
micro	$\mu$	one millionth	$10^{-6}$	$\mu \text{F}$, $\mu \text{A}$
nano	$\text{n}$	one billionth	$10^{-9}$	$\text{nF}$, $\text{nH}$
pico	$\text{p}$	one trillionth	$10^{-12}$	$\text{pF}$

Two details matter particularly in an exam:

• Capital letters matter. $\text{mW}$ is milliwatts, while $\text{MW}$ is megawatts. They differ by a factor of $10^9$.
• Kilo uses a lower-case $\text{k}$. Write $\text{k}\Omega$, not $\text{K}\Omega$.

On meters and some displays, micro may be written as $\text{u}$ where the $\mu$ symbol is unavailable. Thus, $\text{uF}$ commonly means $\mu \text{F}$.

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The reliable method: expand, then rewrite

When you are unsure which way the decimal point should move, do not guess. Use the prefix power of ten.

The method has two parts:

1. Write the starting value in the no-prefix unit.
2. Rewrite that same amount in the requested prefix.

Example: convert $400\text{mA}$ to amperes

Milli means $10^{-3}$, so:

$$400\text{mA}=400\times 10^{-3}\text{A}$$ $$400\text{mA}=0.400\text{A}$$

The current has not become smaller. It is still the same physical current. The number is smaller because one ampere is a larger unit than one milliampere.

Example: convert $2.4\text{kW}$ to watts

Kilo means $10^3$:

$$2.4\text{kW}=2.4\times 10^3\text{W}$$ $$2.4\text{kW}=2400\text{W}$$

Here the number becomes larger because watts are smaller units than kilowatts.

A useful sense check is:

• Converting to a larger unit gives a smaller number.
• Converting to a smaller unit gives a larger number.

For instance, $\text{A}$ is larger than $\text{mA}$, so $400\text{mA}$ must be less than $400\text{A}$. Likewise, $\text{nF}$ is smaller than $\mu \text{F}$, so a capacitance written in nanofarads will have a larger number.

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Converting directly between two prefixed units

You will often need to convert between two prefixed forms, such as $\text{k}\Omega$ and $\text{M}\Omega$, or $\mu \text{F}$ and $\text{nF}$.

The safest approach remains to pass through the no-prefix unit. After practice, you can use the exponents directly.

Suppose the starting prefix has exponent $p$, and the target prefix has exponent $q$. If the starting number is $N_s$, the target number is:

$$N_t=N_s\times 10^{p-q}$$

You do not need to treat this as a new formula to memorise. It is simply a compact way to compare the two prefix powers.

Example: convert $0.82\text{M}\Omega$ to $\text{k}\Omega$

Mega is $10^6$ and kilo is $10^3$.

$$0.82\text{M}\Omega =0.82\times 10^6\Omega$$ $$0.82\times 10^6\Omega =820000\Omega$$

Since:

$$1\text{k}\Omega =10^3\Omega$$

the result is:

$$0.82\text{M}\Omega =820\text{k}\Omega$$

Using the direct exponent check:

$$0.82\times 10^{6-3}=0.82\times 10^3=820$$

Therefore:

$$0.82\text{M}\Omega =820\text{k}\Omega$$

Example: convert $0.047\mu \text{F}$ to $\text{nF}$

Micro is $10^{-6}$, and nano is $10^{-9}$.

$$0.047\mu \text{F}=0.047\times 10^{-6}\text{F}$$

To express that quantity in nanofarads:

$$0.047\times 10^{-6}\text{F}=47\times 10^{-9}\text{F}$$

Therefore:

$$0.047\mu \text{F}=47\text{nF}$$

A quick check confirms the direction: nanofarads are smaller than microfarads, so the numerical value should increase from $0.047$ to $47$.

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Calculator use and written working

For conversion questions, the calculator is useful, but your setup protects you from a wrong entry. Write the prefix factor before reaching for the calculator.

For example, to convert $35\mu \text{A}$ to $\text{A}$:

$$35\mu \text{A}=35\times 10^{-6}\text{A}$$ $$35\mu \text{A}=0.000035\text{A}$$

On a scientific calculator, this is often entered as:

$$35\times 10^{-6}$$

Many calculators also have an $\text{EXP}$ or $\text{EE}$ key, which represents “multiply by ten to a power.” Check your own calculator before the exam so you can enter negative exponents confidently.

For written calculation marks, use a layout like this:

$$\begin{array}{rl}I& =150\text{mA}\\ & =150\times 10^{-3}\text{A}\\ & =0.150\text{A}\end{array}$$

This shows the marker that you understood the prefix even if a calculator slip occurs on the final number.

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Electrical examples you should recognise quickly

These are equivalent ways to write the same quantities:

Quantity	Equivalent forms
Current	$5\text{A}=5000\text{mA}$
Current	$0.025\text{A}=25\text{mA}$
Resistance	$6800\Omega =6.8\text{k}\Omega$
Resistance	$2.2\text{M}\Omega =2200\text{k}\Omega$
Power	$1500\text{W}=1.5\text{kW}$
Capacitance	$0.1\mu \text{F}=100\text{nF}$
Frequency	$500000\text{Hz}=500\text{kHz}$

The key is always to convert the unit and number together. Do not change only the number or only the prefix.

For example, these statements are not equivalent:

$$4.7\Omega \ne 4.7\text{k}\Omega$$

But this statement is correct:

$$4.7\text{k}\Omega =4700\Omega$$

Later, when you substitute values into electrical formulas, it is usually safest to use no-prefix units unless the formula sheet or question explicitly tells you otherwise. Thus, convert $\text{mA}$ to $\text{A}$, $\text{k}\Omega$ to $\Omega$, and $\text{kW}$ to $\text{W}$ before calculation. You can then convert the final answer into a more convenient prefix if required.

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A short exam routine for prefixes

When you see a prefixed value in a question, use this routine:

1. Copy the given value exactly, including its prefix. For example, write $I=250\text{mA}$, not $I=250\text{A}$.
2. Identify the required unit. The question might request $\text{A}$, $\text{mA}$, $\Omega$, or $\text{k}\Omega$.
3. Write the prefix power of ten for the starting value and, if needed, the target value.
4. Show one conversion line before entering the number in the calculator.
5. Use the unit-size check. If changing to a smaller unit, the number should rise; if changing to a larger unit, it should fall.
6. Put the requested unit on the final answer.

The most common mistakes are predictable:

• Treating $\text{m}$ and $\text{M}$ as the same prefix.
• Forgetting that micro is $10^{-6}$, not $10^{-3}$.
• Moving the decimal point in the wrong direction.
• Reporting a correct number with the wrong unit.
• Entering a prefixed value directly into a formula that expects no-prefix units.

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Key takeaways

SI prefixes let you express the same electrical quantity at a convenient scale.

• $\text{k}$ means $10^3$, $\text{M}$ means $10^6$, and $\text{G}$ means $10^9$.
• $\text{m}$ means $10^{-3}$, $\mu$ means $10^{-6}$, $\text{n}$ means $10^{-9}$, and $\text{p}$ means $10^{-12}$.
• Prefix symbols are case-sensitive: $\text{mW}$ and $\text{MW}$ are vastly different quantities.
• The physical quantity stays unchanged during a conversion; only its numerical representation changes.
• If uncertain, replace the prefix with its power of ten, convert through the no-prefix unit, and check whether the number should get larger or smaller.

Next, you will use these conversion skills while evaluating formula-sheet expressions involving fractions, percentages, powers of ten, squares, and roots.