The decimal representation of -$\frac{16}{45}$

Question

Accepted Answer

The correct answer to the question is Option 4: -0.3$\overline5$. Let's provide a detailed explanation to justify why this is the correct answer and why the other options are incorrect.

### Explanation for Option 4:

1. **Conversion of Fraction to Decimal:**
   - The fraction given is -$\frac{16}{45}$. To convert this fraction into a decimal, we perform the division of 16 by 45.
   - When you divide 16 by 45, the result is approximately -0.355555..., which can be expressed as -0.3$\overline5$, indicating that the digit 5 repeats indefinitely.

2. **Negative Sign:**
   - The fraction is negative, as indicated by the negative sign in -$\frac{16}{45}$. Therefore, the decimal representation must also be negative.

3. **Repeating Decimal:**
   - The repeating part of the decimal is 5, which is correctly represented in the notation -0.3$\overline5$.

### Explanation for Why Other Options are Incorrect:

1. **Option 1: 0.350.3$\overline5$**
   - This option is incorrect because it represents a positive decimal, whereas the fraction -$\frac{16}{45}$ is negative. Additionally, the notation "0.350.3$\overline5$" is not a standard representation of a decimal.

2. **Option 2: 1.3$\overline5$**
   - This option is incorrect because it represents a positive number greater than 1. The fraction -$\frac{16}{45}$ is negative and less than 1 in absolute value, so this option does not match the correct decimal representation.

3. **Option 3: -1.3$\overline5$**
   - This option is incorrect because it represents a negative number greater than 1 in absolute value. The fraction -$\frac{16}{45}$ is less than 1 in absolute value, so this option does not accurately represent the fraction.

In conclusion, Option 4: -0.3$\overline5$ is the correct representation of the decimal form of -$\frac{16}{45}$, as it accurately reflects the negative sign and the repeating decimal pattern.