Measurement

Scientific Notation, Prefixes and Conversion

Scientific Notation, Prefixes and Conversion

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

$$1 \leq a < 10$$

$$\text{n = integers}$$

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

1 kg = 1000 gram

1 kg = 10 ons

1 kg = 2 pon

1 ons = 100 gram

1 ton = 1000 kg

1 liter = 1 dm3 = 0.001 m3

1 liter = 1000 cm3 = 1000 cc

1 ml = 1 cm3 = 0.001 liter

1 minute = 60 seconds

1 hour = 60 minutes = 3600 seconds

1 day = 24 hours