To identify the rational numbers from the given list, we first recall that a rational number is any number that can be expressed as the ratio of two integers (a fraction), including terminating decimals and repeating decimals.

Analysis of each number:

• $\sqrt{2}$ (A): Irrational. It's a non-terminating, non-repeating decimal.
• $-5.39$ (B): Rational. It is a terminating decimal and can be written as $-\frac{539}{100}$.
• $-14$ (C): Rational. It is an integer, which can be expressed as $\frac{-14}{1}$.
• $0$ (D): Rational. It is an integer, which can be expressed as $\frac{0}{1}$.
• $0.08\overline{3}$ (E): Rational. This is a repeating decimal and can be written as a fraction $\frac{83}{1000}$.
• $\sqrt{4}$ (F): Rational. $\sqrt{4} = 2$, which is an integer, and can be written as $\frac{2}{1}$.
• $9.12112111211112 \ldots$ (G): Irrational. This is a non-repeating, non-terminating decimal.
• $15.999$ (H): Rational. It is a terminating decimal and can be written as $\frac{15999}{1000}$.
• $\frac{19}{47}$ (I): Rational. It is a fraction of two integers.
• $-\sqrt{11}$ (J): Irrational. It is a non-terminating, non-repeating decimal.
• $2424$ (K): Rational. It is an integer, which can be written as $\frac{2424}{1}$.
• $-\frac{3}{8}$ (L): Rational. It is a fraction of two integers.

Rational numbers in the list are:

• B. $-5.39$
• C. $-14$
• D. $0$
• E. $0.08\overline{3}$
• F. $\sqrt{4} = 2$
• H. $15.999$
• I. $\frac{19}{47}$
• K. $2424$
• L. $-\frac{3}{8}$

Thus, the correct answers are B, C, D, E, F, H, I, K, and L.

Would you like further details or have any questions?

Related questions:

1. What makes a number irrational?
2. Can all repeating decimals be expressed as rational numbers?
3. How can we determine if a square root results in a rational number?
4. What is the difference between a terminating and a repeating decimal?
5. How do we convert a repeating decimal to a fraction?

Tip:

Rational numbers can always be expressed as fractions, so check if a decimal terminates or repeats to confirm if it’s rational.