The third proportional to 0.8 and 0.2 is :

Options

A. 0.05
B. 0.8
C. 0.4
D. 0.032

Answer

To find the third proportional to the numbers 0.8 and 0.2, we can follow these steps:

### Step 1: Understand the concept of third proportional
The third proportional to two numbers A and B is a number C such that the ratio of A to B is the same as the ratio of B to C. This can be expressed mathematically as:
\[ \frac{A}{B} = \frac{B}{C} \]

### Step 2: Set up the equation
Given A = 0.8 and B = 0.2, we can set up the equation:
\[ \frac{0.8}{0.2} = \frac{0.2}{C} \]

### Step 3: Cross-multiply to solve for C
Cross-multiplying gives us:
\[ 0.8 \cdot C = 0.2 \cdot 0.2 \]

### Step 4: Calculate the right side
Calculating the right side:
\[ 0.2 \cdot 0.2 = 0.04 \]

### Step 5: Substitute back into the equation
Now we have:
\[ 0.8C = 0.04 \]

### Step 6: Solve for C
To find C, divide both sides by 0.8:
\[ C = \frac{0.04}{0.8} \]

### Step 7: Perform the division
Calculating the division:
\[ C = 0.05 \]

### Conclusion
Thus, the third proportional to 0.8 and 0.2 is **0.05**.

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