Yes, \( 6.353535 \) is a rational number. Rational numbers are defined as numbers that can be expressed as the quotient of two integers (i.e., in the form \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \)).
The number \( 6.353535 \) can be expressed as \( 6.35\overline{35} \), which is a repeating decimal. To convert it to a fraction, we can let \( x = 6.353535 \).
We can manipulate this repeating decimal:
- Multiply by \( 100 \) to shift the decimal two places: \[ 100x = 635.353535 \]
- Now, subtract the original \( x \) from this equation: \[ 100x - x = 635.353535 - 6.353535 \] Simplifying gives: \[ 99x = 629 \]
- Solving for \( x \): \[ x = \frac{629}{99} \]
Since \( 629 \) and \( 99 \) are both integers and \( 99 \neq 0 \), \( 6.353535 \) is indeed a rational number.