Find the fourth proportional to :
0.6, 1.5, 3

Answer

To find the fourth proportional to the numbers 0.6, 1.5, and 3, we can follow these steps:

### Step-by-Step Solution:

1. **Set Up the Proportion**:
We need to express the relationship between the numbers using a proportion. We can write it as:
\[ 0.6 : 1.5 :: 3 : x \]
This means that the ratio of 0.6 to 1.5 is the same as the ratio of 3 to \( x \).

2. **Write the Proportion as an Equation**:
From the proportion, we can set up the equation:
\[ \frac{0.6}{1.5} = \frac{3}{x} \]

3. **Cross Multiply**:
To solve for \( x \), we can cross-multiply:
\[ 0.6 \cdot x = 3 \cdot 1.5 \]

4. **Calculate the Right Side**:
Now, calculate \( 3 \cdot 1.5 \):
\[ 3 \cdot 1.5 = 4.5 \]
So, the equation becomes:
\[ 0.6 \cdot x = 4.5 \]

5. **Solve for \( x \)**:
To find \( x \), divide both sides of the equation by 0.6:
\[ x = \frac{4.5}{0.6} \]

6. **Perform the Division**:
Now, calculate \( \frac{4.5}{0.6} \):
- To simplify, we can multiply the numerator and denominator by 10 to eliminate the decimal:
\[ x = \frac{45}{6} \]
- Now, divide 45 by 6:
\[ 45 \div 6 = 7.5 \]

7. **Conclusion**:
Therefore, the fourth proportional to 0.6, 1.5, and 3 is:
\[ x = 7.5 \]