e) The recurring decimal is:

e) The recurring decimal is: A recurring decimal is a decimal in which one or more digits repeat infinitely. i) 3.4444...: The digit 4 repeats indefinitely. This is a recurring decimal. ii) 2.34178...: The ellipsis indicates continuation, but no repeating pattern is shown. iii) 0.23142...: No repeating pattern is shown. iv) 3.0014...: No repeating pattern is shown. The correct option is i). i) 3.4444... f) Multiplicative identity for the set of real numbers is: The multiplicative identity is the number that, when multiplied by any real number, leaves the number unchanged. For real numbers, this is 1. i) 0: This is the additive identity. ii) 1: For any real number x, x × 1 = x. iii) -1: Multiplying by -1 changes the sign of the number. iv) (1)/(2): This is not the multiplicative identity. The correct option is ii). ii) 1 g) The additive inverse of (3)/(8) is: The additive inverse of a number x is the number -x such that x + (-x) = 0. For (3)/(8), the additive inverse is -(3)/(8). i) -(8)/(3): This is the negative reciprocal. ii) -(3)/(8): This is the additive inverse. iii) (3)/(8): This is the original number. iv) 0: This is the additive identity. The correct option is ii). ii) -(3)/(8) h) Which of these is an irrational number? An irrational number is a number that cannot be expressed as a simple fraction (p)/(q) where p and q are integers and q ≠ 0. Square roots of non-perfect squares are irrational. i) sqrt(5): Since 5 is not a perfect square, sqrt(5) is an irrational number. ii) sqrt(9) = 3: This is a rational number (3 = (3)/(1)). iii) sqrt(4) = 2: This is a rational number (2 = (2)/(1)). iv) sqrt(36) = 6: This is a rational number (6 = (6)/(1)). The correct option is i). i) sqrt(5) That's 2 down. 3 left today — send the next one.