How to turn mixed cyclic decimals into fractions?

Method of converting mixed cyclic decimal into fraction:

Mixed cycle decimal, there are several numbers in the cycle segment and several 9' s in the denominator; There are several numbers that are not cyclic, so add a few zeros to the denominator; A molecule is the number of nodes that never cycle to a cycle minus the number of nodes that never cycle. The calculation method is as follows:

Solution:

(1), 1.4727 ... (Cycle node is "27")

1.42 27 27 27……

= 1+0.4227 ..

= 1+(4227-42)/9900

= 1+4 185/9900

= 1+837/ 1980

= 1 and 837/ 1980

(2), 0.003 1 31... (the number of circulating nodes is "31")

0.003 1 3 1 3 1 .....

=3 1/9900

(3), 2.04352 1 521521... (the number of circulating nodes is "521")