Check whether the following numbers are in proportion or not :
3.6, 0.4, 4.5, 0.5

Answer

To determine if the numbers 3.6, 0.4, 4.5, and 0.5 are in proportion, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the numbers**: We have four numbers:
- \( a = 3.6 \)
- \( b = 0.4 \)
- \( c = 4.5 \)
- \( d = 0.5 \)

2. **Set up the proportion condition**: The numbers are in proportion if:
\[ \frac{a}{b} = \frac{c}{d} \]

3. **Calculate \( \frac{a}{b} \)**:
\[ \frac{a}{b} = \frac{3.6}{0.4} \]
To simplify this, we can multiply both the numerator and the denominator by 10 to eliminate the decimal:
\[ \frac{3.6 \times 10}{0.4 \times 10} = \frac{36}{4} = 9 \]
Thus,
\[ \frac{a}{b} = 9 \]

4. **Calculate \( \frac{c}{d} \)**:
\[ \frac{c}{d} = \frac{4.5}{0.5} \]
Similarly, we can multiply both the numerator and the denominator by 10:
\[ \frac{4.5 \times 10}{0.5 \times 10} = \frac{45}{5} = 9 \]
Thus,
\[ \frac{c}{d} = 9 \]

5. **Compare the two ratios**: Now we compare the two results:
\[ \frac{a}{b} = 9 \quad \text{and} \quad \frac{c}{d} = 9 \]

6. **Conclusion**: Since both ratios are equal:
\[ \frac{a}{b} = \frac{c}{d} \]
Therefore, the numbers 3.6, 0.4, 4.5, and 0.5 are in proportion.