Question

The continued fraction for 118/303 is:
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Answer 1

Step-by-step explanation:

We can write 118/303 as 1/(303/118) →

118/303 = 1/(303/118) = 1/A

A = 303/118 = 2+67/118 = 2+1/(118/67) = 2+1/B

B = 118/67 = 1+51/67 = 1+1/(67/51) = 1+1/C

C = 67/51 = 1+16/51 = 1+1/(51/16) = 1+1/D

D = 51/16 = 3+3/16 = 3+1/(16/3) = 3+1/E

E = 16/3 = 5+1/3 ←At last We got 1 as remainder

Now,

Answer→ 118/303 = 1/[2+1/{1+1/(1+1/(3+1/(5+1/3)))}

Answer 2

Answer:

We can write 118/303 as 1/(303/118) →

118/303 = 1/(303/118) = 1/A

A = 303/118 = 2+67/118 = 2+1/(118/67) = 2+1/B

B = 118/67 = 1+51/67 = 1+1/(67/51) = 1+1/C

C = 67/51 = 1+16/51 = 1+1/(51/16) = 1+1/D

D = 51/16 = 3+3/16 = 3+1/(16/3) = 3+1/E

E = 16/3 = 5+1/3 ←At last We got 1 as remainder

Answer→ 118/303 = 1/[2+1/{1+1/(1+1/(3+1/(5+1/3))}