1. **Stating the problem:** We need to compare the decimal number $0.398$ with the fraction $\frac{2}{5}$ and determine which of the statements is true:
- $0.398 > \frac{2}{5}$
- $0.398 < \frac{2}{5}$
- $0.398 = \frac{2}{5}$
2. **Convert the fraction to decimal:** To compare easily, convert $\frac{2}{5}$ to decimal using the formula:
$$\text{Decimal} = \frac{\text{Numerator}}{\text{Denominator}} = \frac{2}{5}$$
Calculate:
$$\frac{2}{5} = 0.4$$
3. **Compare the two decimals:** Now compare $0.398$ and $0.4$:
- $0.398$ is less than $0.4$ because $0.398 < 0.4$
4. **Conclusion:** Therefore, the true statement is:
$$0.398 < \frac{2}{5}$$
which corresponds to statement 2.
**Final answer:** Statement 2 is true.
Decimal Fraction Comparison 7C7A1A
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.