The question asks us to find the range in which the value of \(x\) lies, where \(x\) is defined by the continued fraction:
\( x = \frac{1}{2 + \frac{3}{4 + \frac{5}{6 + \frac{7}{8 + \frac{9}{10}}}}} \)
To determine the range, we evaluate the continued fraction step by step, starting from the innermost part and working outward. This method helps us approximate the value of \(x\) accurately.
The approximate value of \(x\) is \(0.3797\). Comparing with the given options:
Upper bound:
Lower bound:
Thus, we obtain:
\( 0.3636 < x < 0.3797 \)
The value of \(x\) lies in the range:
\( 0 < x < 0.5 \)
Hence, the correct option is \(0 < x < 0.5\).
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
Number 0.232323 can be written in rational form as:
Solve: \(\frac{1}{2}\) [{-2(2 + 3)*20}/2]
Match the following.
Column I | Column II | ||
a. | Equivalent fraction of \(\frac{7}{12}\) is | i. | Proper fraction |
b. | Equivalent fraction of \(\frac{9}{15}\) is | ii. | Improper fraction |
c. | \(\frac{7}{11}\) is | iii. | \(\frac{21}{36}\) |
d. | \(\frac{19}{5}\) is | iv. | \(\frac{3}{5}\) |
Among the fractions \(\frac{7}{12}\) , \(\frac{8}{15}\) , \(\frac{17}{24}\) and \(\frac{13}{18}\) , which is the smallest?