Question

Note: -

The continued fraction for118/303 is

a) [2;1,1,3,5,3]

b) [2,1,1,3,5,7]

c) [0;2,1,1,3,5,7]

d) [0:2,1,1,3,5,3]​

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:

The continued fraction for 118/303 is a) [2,1,1,3,5,3]

Continued Fraction:

• A continuing fraction is an expression in mathematics that is generated by iteratively portraying a number as the sum of its integer component and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.
• The iteration/recursion in a finite continued fraction (or ended continued fraction) is terminated after a finite number of steps by using an integer instead of another continued fraction.
• An infinite continuing fraction, on the other hand, is an endless expression.
• In either scenario, except for the first, all integers in the series must be positive.
• The numbers are known as the coefficients or terms of the continuing fraction.

Step-by-step explanation:

We can write $\frac{118}{303}$ as $\frac{1}{\frac{118}{303} }$ →

$\frac{1}{\frac{118}{303} } = \frac{303}{118} = A$

$A= \frac{303}{118} = 2+\frac{67}{118} = 2+\frac{1}{B}$

$B= \frac{118}{67} = 1+\frac{51}{67} =1+ \frac{1}{\frac{67}{51}} =1+\frac{1}{C}$

$C= \frac{67}{51} = 1+\frac{16}{51} =1+ \frac{1}{\frac{51}{16}} =1+\frac{1}{D}$

$D= \frac{51}{16} = 3+\frac{3}{16} =3+ \frac{1}{\frac{16}{3}} =3+\frac{1}{E}$

$E=\frac{16}{3} = 5+\frac{1}{3}$

E = 16/3 = 5+1/3

Remainder= 1

Now,

Thus, the answer [2,1,1,3,5,3] is correct.

The explanation for not chosen parts

The calculation is different than the answer mentioned in other options.

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