To **add or subtract numbers in standard form**, convert them into decimal notation, do the operation and convert them back. You can also isolate the power of ten with the lowest exponent to make the calculation simpler.

\begin{align*} \Tblue{3.6} \times 10^\Tred{3} + \Tblue{7.1} \times 10^\Tred{2}= 3600 + 710 = 4310 & = \Tblue{4.31} \times 10^\Tred{3}\\ \qquad= \Tblue{36}\times 10^\Tred{2} + \Tblue{7.1}\times 10^\Tred{2} = \Tblue{43.1}\times 10^\Tred{2} & = \Tblue{4.31}\times 10^\Tred{3} \end{align*}

To **multiply or divide numbers in standard form**, use the laws for indices. Indices are added for multiplication and subtracted for division.

\begin{align*} (\Tblue{6.2} \times 10^\Tred{5}) \times (\Tblue{3.1} \times 10^\Tred{2}) &= (\Tblue{6.2\times 3.1}) \times 10^{\Tred{5+2}}\\ &= \Tblue{19.22} \times 10^\Tred{7}\\ &= \Tblue{1.922} \times 10^\Tred{8}\\ (\Tblue{6.2} \times 10^\Tred{5}) \div (\Tblue{3.1} \times 10^\Tred{2}) &= (\Tblue{6.2 \div 3.1}) \times 10^{\Tred{5-2}} \\ &= \Tblue{2} \times 10^\Tred{3} \end{align*}