SL 1.1—Using standard form

Standard Form: A way of writing any number as $a\times 10^n$, where $1\le a<10$ and $n$ is an integer. Also called scientific notation.

Standard form is essential whenever numbers become inconveniently large or small in decimal notation. Instead of writing out 602,200,000,000,000,000,000,000 (Avogadro's number), scientists write $6.022\times 10^{23}$. Instead of 0.000000000911 kg (the mass of an electron), physicists write $9.11\times 10^{-31}$ kg.

The two parts of standard form each carry distinct information:

• $a$ , captures the significant figures of the number (always at least 1 but strictly less than 10)
• $10^n$ , sets the scale, telling you how large or small the number is