Final answer:
Isabel's claim that 1/7 is not a rational number is incorrect. The fact that its decimal form is non-terminating but repeating (0.142857...) confirms that it is rational, as it can be expressed as a fraction. The rules of mathematics and an understanding of repeating decimals demonstrate its rationality.
Step-by-step explanation:
Isabel is incorrect in stating that 1/7 is not a rational number because its decimal form neither terminates nor repeats. A rational number is defined as a number that can be expressed as a ratio of two integers, where the denominator is not zero. Since 1/7 fits this definition, it is indeed a rational number. Although the decimal form of 1/7 is a non-terminating, repeating decimal (0.142857142857...), this fact does not make it irrational. An irrational number is one that cannot be expressed as a simple fraction, and its decimal form does not repeat or terminate. Since the decimal form of 1/7 has a repeating pattern, it is a clear indication of it being rational.
The concept that the rules of mathematics are universal and objective applies here. Regardless of the representation (fraction or decimal), the nature of the number does not change. Understanding this will help you to realize that even if a decimal looks complex, as long as there's a pattern or it can be expressed as a fraction, it is rational. This grounding in basic arithmetic principles and patterns solidifies our understanding of rational numbers.
Using a calculator might sometimes be misleading if the user doesn't understand the nature of numbers. Calculators will show many decimal places, but that doesn't imply the number is irrational. When dealing with non-terminating decimals, we have to look for repeating patterns to determine if the number is rational, which is the case with 1/7.
Additionally, in mathematics, we learn that dividing by a number is the same as multiplying by its reciprocal. For 1/7, this means multiplying 1 by 1/7, which will always result in a repeating decimal; this repeating nature is predictable for such fractions. Thus, even without a calculator, the rules of mathematics tell us that 1/7 must be a rational number.