Question

Represent the following mixed infinite decimal periodic fractions as common fractions:
Arrange the following numbers in an increasing order.
$1;0.37;\frac{65}{63};\frac{61}{59};$ $\tan {33}^{\circ }$; $\tan (-{314}^{\circ })$.

Answer 1

Given number are

$1;0.37;\frac{65}{63};\frac{61}{59};\tan \left({33}^0\right);\tan (-{314}^0)$

$\frac{65}{63}=1.031746032$

$\frac{61}{59}=1.0338998305$

$\tan \left({33}^0\right)=0.649407593$

$\tan (-{314}^0)=1.035530314$

So the arrangement in increassing order is

$0.37;\tan \left({33}^0\right);1;\frac{65}{63};\frac{61}{59};\tan (-{314}^0)$