Operations with Standard Form
Work fluently with scientific notation.
Standard form
\[a\times 10^n,\quad 1\le a<10\]
Multiplication and division
Multiply or divide the front numbers, then use laws of indices on the powers of 10.
Worked example
Simplify \((3\times10^5)(4\times10^3)\).
\[(3\times4)\times10^{5+3}=12\times10^8=1.2\times10^9.\]
Worked example
Simplify \(\frac{8\times10^6}{2\times10^2}\).
\[\frac82\times10^{6-2}=4\times10^4.\]