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Scientific Notation

Scientific notation is a way of expressing numbers that are either very large or very small in a short and convenient form. The scientific notation takes the following form:

M⋅10nM \cdot 10^n

where MM is the so-called significand or mantissa and is multiplied with 10 to the power of nn the exponent. If the number is negative then a minus sign precedes the mantissa MM.

2=2⋅100300=300⋅100=30⋅101=3⋅102\begin{align*} 2 &= 2 \cdot 10^0 \\ 300 &= 300 \cdot 10^0 = 30 \cdot 10^1 = 3 \cdot 10^2 \end{align*}

Normalized Notation​

As you can see in the second example there can be some ambiguity which is why the normalized notation was introduced. In the normalized form the exponent is chosen so that the mantissa is at least 1 but less than 10, so M∈[1,10)M \in [1,10).

2=2⋅100300=3⋅102−53′000=−5.3⋅1040.2=2⋅10−1\begin{align*} 2 &= 2 \cdot 10^0 \\ 300 &= 3 \cdot 10^2 \\ -53'000 &= -5.3 \cdot 10^4 \\ 0.2 &= 2 \cdot 10^{-1} \end{align*}

Engineering Notation​

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E Notation​

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