Multiplication and division in standard form

Calculate the coefficients and use index laws on the powers of ten. Finish by normalising the coefficient to the interval \(1\le A<10\).

Example

\(\begin{aligned}(6\times10^5)(4\times10^{-3})&=24\times10^2\\&=2.4\times10^3\end{aligned}\)

\(\begin{aligned}\dfrac{3.6\times10^7}{8\times10^2}&=0.45\times10^5\\&=4.5\times10^4\end{aligned}\)

When a coefficient is multiplied by \(10\), reduce the exponent by \(1\) to preserve the value. When it is divided by \(10\), increase the exponent by \(1\).