Question 4.2.21

We might be interested in the ratio between terms in the Fibonacci sequence. Find to three decimal places:

1. $34\div21$ Show answer

   \begin{align*}\longdiv{\ms{3}\ms{4.}\ms{0}\ms{0}\ms{0}\ms{0}}{21}{\ms{}\ms{1.}\ms{6}\ms{1}\ms{9}\ms{0}}{\\&\underline{\ms{2}\ms{1}}\\&\ms{1}\ms{3}\ms{0}\\&\underline{\ms{1}\ms{2}\ms{6}}\\&\ms{}\ms{}\ms{4}\ms{0}\\&\ms{}\ms{}\underline{\ms{2}\ms{1}}\\&\ms{}\ms{}\ms{1}\ms{9}\ms{0}\\&\ms{}\ms{}\underline{\ms{1}\ms{8}\ms{9}}\\&\ms{}\ms{}\ms{}\ms{}\ms{1}\ms{0}}\end{align*} So $34\div21 = 1.619$

   

2. $55\div34$ Show answer

   \begin{align*}\longdiv{\ms{5}\ms{5.}\ms{0}\ms{0}\ms{0}\ms{0}}{34}{\ms{}\ms{1.}\ms{6}\ms{1}\ms{7}\ms{6}}{\\&\underline{\ms{3}\ms{4}}\\&\ms{2}\ms{1}\ms{0}\\&\underline{\ms{2}\ms{0}\ms{4}}\\&\ms{}\ms{}\ms{6}\ms{0}\\&\ms{}\ms{}\underline{\ms{3}\ms{4}}\\&\ms{}\ms{}\ms{2}\ms{6}\ms{0}\\&\ms{}\ms{}\underline{\ms{2}\ms{3}\ms{8}}\\&\ms{}\ms{}\ms{}\ms{2}\ms{2}\ms{0}}\end{align*} So $55\div34 = 1.618$

   

3. $89\div55$ Show answer

   \begin{align*}\longdiv{\ms{8}\ms{9.}\ms{0}\ms{0}\ms{0}\ms{0}}{55}{\ms{}\ms{1.}\ms{6}\ms{1}\ms{8}\ms{1}}{\\&\underline{\ms{5}\ms{5}}\\&\ms{3}\ms{4}\ms{0}\\&\underline{\ms{3}\ms{3}\ms{0}}\\&\ms{}\ms{1}\ms{0}\ms{0}\\&\ms{}\ms{}\underline{\ms{5}\ms{5}}\\&\ms{}\ms{}\ms{4}\ms{5}\ms{0}\\&\ms{}\ms{}\underline{\ms{4}\ms{4}\ms{0}}\\&\ms{}\ms{}\ms{}\ms{1}\ms{0}\ms{0}}\end{align*} So $89\div55 = 1.618$