Answer:
To convert the repeating decimal \( 2.7\overline{435} \) into a rational form, follow these steps:
Let's denote \( x = 2.7\overline{435} \).
1. Identify the repeating part: \( 2.7\overline{435} \) means that the digits "435" repeat indefinitely.
2. Express \( x \) as:
\[ x = 2.743543543... \]
3. Multiply \( x \) by \( 1000 \) (since there are three digits in the repeating part "435"):
\[ 1000x = 2743.543543... \]
4. Subtract the original \( x \) from \( 1000x \) to eliminate the repeating part:
\[ 1000x - x = 2743.543543... - 2.743543543... \]
\[ 999x = 2740 \]
5. Solve for \( x \):
\[ x = \frac{2740}{999} \]
6. Simplify the fraction \( \frac{2740}{999} \), if possible. Since 2740 and 999 have no common factors other than 1, \( \frac{2740}{999} \) is already in its simplest form.
Therefore, the rational form of \( 2.7\overline{435} \) is \( \boxed{\frac{2740}{999}} \).
Thus, the rational form of
Step-by-step explanation:
2.7 overline (435) is
[tex] \frac{4568}{1665} [/tex]
