Question

A metre is $39.37079$ inches, shew by the theory of continued fractions that $32$ metres is nearly equal to $35yards$.

Answer 1

To show that $32$ metres is nearly equal to $35$ yards

As we know,

$1metre=39.37079\times \frac{1}{36}$ yards

$=1.0936$ yards

Also,

$1.0936=1+\frac{1}{10+}\frac{1}{1+}\frac{1}{2+}\frac{1}{6+}\frac{1}{6}$

$\therefore$ The convergents are

$1,\frac{11}{10},\frac{12}{11},\frac{35}{32},.....$

Thus, $32$ metres nearly equal to 35 yards.