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# Arithmetic in standard form

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*}

Large numbers are often given in standard form. How far is Saturn from Earth?