Scientific Notation, Prefixes, and Conversion

SCIENTIFIC NOTATION

 

\(\large \bbox [5px, border: 2px solid red]{a \times 10^{\text{n}}}\)

\(1 \leq a < 10\)

\(\text{n = integers}\)

 

Example 1

\(\text{a.}\:\:\:598 000 000 = 5.98 \times 10^8\)

\(\text{b.}\:\:\:0.0000652 = 6.52 \times 10^{-5}\)

 

Example 2

\(\text{a.}\:\:\:30 000\text{ m} + 24000 \text{ m}\)

\(\:\:\:\:\:\:\:3.0 \times 10^4 \text{ m} + 2.4 \times 10^4 \text{ m}\)

\(\:\:\:\:\:\:\:5.4 \times 10^4 \text{ m}\)

 

\(\text{b.}\:\:\:0.00856\text{ mm}- 0.00078 \text{ mm}\)

\(\:\:\:\:\:\:\:8.56 \times 10^{-3} \text{ mm} - 7.8 \times 10^{-4}\text{ mm}\)

\(\:\:\:\:\:\:\:8.56 \times 10^{-3} \text{ mm} - 0.78 \times 10^{-3}\text{ mm}\)

\(\:\:\:\:\:\:\:7.78 \times 10^{-3}\text{ mm}\)

PREFIXES

 

\begin{array}{cccc}
\color{blue}\text{Prefix} && \color{blue}\text{Symbol} &&\color{blue} \text{Factor of 10}\\\\
\text{peta} && \text{P} && 10^{15}\\\\
\text{tera} && \text{T} && 10^{12}\\\\
\text{giga} && \text{G} && 10^{9}\\\\
\text{mega} && \text{M} && 10^{6}\\\\
\text{kilo} && \text{k} && 10^{3}\\\\
\text{hecto} && \text{h} && 10^{2}\\\\
\text{deca} && \text{da} && 10^{1}\\\\
\text{deci} && \text{d} && 10^{-1}\\\\
\text{centi} && \text{c} && 10^{-2}\\\\
\text{milli} && \text{m} && 10^{-3}\\\\
\text{micro} && \mu && 10^{-6}\\\\
\text{nano} && \text{n} && 10^{-9}\\\\
\text{pico} && \text{p} && 10^{-12}
\end{array}

 

Example:

\(2.5 \text{ nm} =\dotso \text{ km}\)

\(\text{nano} = 10^{-9}\)

\(\text{kilo} = 10^3\)

Then subtract the power of 10 of nano to the power of 10 of kilo

\(2.5 \text{ nm} = 2.5 \times 10^{-9-3}\text{ km} = 2.5\times 10^{-12}\text{ km}\)

CONVERSION