Given the following​ numbers, name the rational numbers.
2424​, negative 14−14​, negative 5.39−5.39​, 15.99915.999​, 0.08 3 overbar0.083​, StartFraction 19 Over 47 EndFraction
19
47​, StartRoot 2 EndRoot2​, negative StartRoot 11 EndRoot−11​, StartRoot 4 EndRoot4​, 00​, negative three eighths−
3
8​, 9.12112111211112 ...9.12112111211112...
Question content area bottom
Part 1
Select all that apply.
A.StartRoot 2 EndRoot
StartRoot 2 EndRoot2
B.negative 5.39
negative 5.39−5.39
C.negative 14
negative 14−14
D.0
00
E.0.08 3 overbar
0.08 3 overbar0.083
F.StartRoot 4 EndRoot
StartRoot 4 EndRoot4
G.9.12112111211112 ...
9.12112111211112 ...9.12112111211112...
H.15.999
15.99915.999
I.StartFraction 19 Over 47 EndFraction
StartFraction 19 Over 47 EndFraction
19
47
J.negative StartRoot 11 EndRoot
negative StartRoot 11 EndRoot−11
K.24
2424
L.negative three eighths
negative three eighths−
3
8

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.

Given the following​ numbers, name the rational numbers: 2424​, negative 14−14​, negative 5.39−5.39​, 15.99915.999​, 0.08 3 overbar0.083​, StartFraction 19 Over 47 EndFraction, StartRoot 2 EndRoot, negative StartRoot 11 EndRoot, StartRoot 4 EndRoot, 0​, negative three eighths−3/8, 9.12112111211112...

Identify rational numbers from a list of integers, fractions, and decimals. This problem covers the concepts of rational numbers, irrational numbers, and their properties, with examples involving square roots, fractions, and repeating decimals. Suitable for students in Grades 7-9.

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