Rational Numbers — Statement I-II Type Questions

Statement 1: 1.6666.... can be expressed as a rational number.

Statement 2: A decimal number is said to be non-terminating but recurring decimal if in the decimal part a digit or a group of digits repeats itself again and again.

Which of the following options is correct?

1. Both the statements are true.

2. Both the statements are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Answer

Statement 1 is true, since 1.6666.... is a non-terminating recurring decimal which equals $\dfrac{5}{3}$, a rational number.

Statement 2 is true, as it correctly defines a non-terminating recurring decimal.

Hence, both the statements are true.

Hence, Option 1 is the correct option.