What is the value of $(\frac{(2.3)^3 - 0.027}{(2.3)^2 + 0.69 + 0.09}$

Question

Accepted Answer

To solve the given expression and verify why Option 4 is the correct answer, we need to evaluate the expression step by step:

The expression is:

$$
\frac{(2.3)^3 - 0.027}{(2.3)^2 + 0.69 + 0.09}
$$

**Step 1: Calculate $(2.3)^3$**

$$
(2.3)^3 = 2.3 \times 2.3 \times 2.3 = 12.167
$$

**Step 2: Calculate $(2.3)^2$**

$$
(2.3)^2 = 2.3 \times 2.3 = 5.29
$$

**Step 3: Evaluate the numerator**

$$
(2.3)^3 - 0.027 = 12.167 - 0.027 = 12.14
$$

**Step 4: Evaluate the denominator**

$$
(2.3)^2 + 0.69 + 0.09 = 5.29 + 0.69 + 0.09 = 6.07
$$

**Step 5: Calculate the entire expression**

$$
\frac{12.14}{6.07} \approx 2
$$

Thus, the value of the expression is approximately 2, which corresponds to Option 4.

**Explanation for why other options are incorrect:**

1. **Option 1 (0.3):** The calculated value of the expression is approximately 2, which is significantly larger than 0.3. Therefore, Option 1 is incorrect.

2. **Option 2 (2.3):** Although 2.3 is close to the calculated value, the precise calculation shows that the value is approximately 2, not 2.3. Hence, Option 2 is incorrect.

3. **Option 3 (1):** The calculated value of the expression is approximately 2, which is larger than 1. Therefore, Option 3 is incorrect.

By following the calculations and logical reasoning, we confirm that Option 4 is indeed the correct answer.