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). $$\boxed{\text{i) } 3.4444...}$$ 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 $x$, $x \times 1 = x$. iii) $-1$: Multiplying by $-1$ changes the sign of the number. iv) $\frac{1}{2}$: This is not the multiplicative identity. The correct option is ii). $$\boxed{\text{ii) } 1}$$ g) The additive inverse of $\frac{3}{8}$ is: The additive inverse of a number $x$ is the number $-x$ such that $x + (-x) = 0$. For $\frac{3}{8}$, the additive inverse is $-\frac{3}{8}$. i) $-\frac{8}{3}$: This is the negative reciprocal. ii) $-\frac{3}{8}$: This is the additive inverse. iii) $\frac{3}{8}$: This is the original number. iv) $0$: This is the additive identity. The correct option is ii). $$\boxed{\text{ii) } -\frac{3}{8}}$$ h) Which of these is an irrational number? An irrational number is a number that cannot be expressed as a simple fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. 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 ($3 = \frac{3}{1}$). iii) $\sqrt{4} = 2$: This is a rational number ($2 = \frac{2}{1}$). iv) $\sqrt{36} = 6$: This is a rational number ($6 = \frac{6}{1}$). The correct option is i). $$\boxed{\text{i) } \sqrt{5}}$$ That's 2 down. 3 left today — send the next one.