`(0.3555xx0.5555xx2.025)/(0.225xx1.7775xx0.2222)` is equal to

Options

A. `5.4`
B. `4.58`
C. `4.5`
D. `5.45`

Answer

To solve the expression \((0.3555 \times 0.5555 \times 2.025) / (0.225 \times 1.7775 \times 0.2222)\), we will follow these steps:

### Step 1: Write the expression clearly
We start with the expression:
\[ \frac{0.3555 \times 0.5555 \times 2.025}{0.225 \times 1.7775 \times 0.2222} \]

### Step 2: Count the number of decimal places
Next, we count the number of decimal places in the numerator and denominator:
- In the numerator:
- \(0.3555\) has 4 decimal places
- \(0.5555\) has 4 decimal places
- \(2.025\) has 3 decimal places
- Total = \(4 + 4 + 3 = 11\) decimal places

- In the denominator:
- \(0.225\) has 3 decimal places
- \(1.7775\) has 4 decimal places
- \(0.2222\) has 4 decimal places
- Total = \(3 + 4 + 4 = 11\) decimal places

### Step 3: Remove the decimals
To eliminate the decimals, we multiply both the numerator and denominator by \(10^{11}\):
\[ \frac{0.3555 \times 0.5555 \times 2.025 \times 10^{11}}{0.225 \times 1.7775 \times 0.2222 \times 10^{11}} = \frac{3555 \times 5555 \times 2025}{225 \times 17775 \times 2222} \]

### Step 4: Simplify the fractions
Now we can simplify the fractions. Let's factor out common terms:
- \(3555\) can be expressed as \(5 \times 711\)
- \(5555\) can be expressed as \(5 \times 1111\)
- \(2025\) can be expressed as \(5 \times 405\)
- \(225\) can be expressed as \(15^2\)
- \(17775\) can be expressed as \(5 \times 3555\)
- \(2222\) can be expressed as \(2 \times 1111\)

### Step 5: Cancel out common factors
Now we can cancel out the common factors:
\[ \frac{(5 \times 711) \times (5 \times 1111) \times (5 \times 405)}{(15^2) \times (5 \times 3555) \times (2 \times 1111)} \]
Cancelling \(5\) and \(1111\) from both numerator and denominator:
\[ \frac{711 \times 5 \times 405}{15^2 \times 3555 \times 2} \]

### Step 6: Further simplification
Now we can simplify:
- \(15^2 = 225\)
- \(3555 = 5 \times 711\)

After simplifying, we get:
\[ \frac{711 \times 5 \times 405}{225 \times 5 \times 711} = \frac{405}{225} \]

### Step 7: Final simplification
Now, we simplify \(\frac{405}{225}\):
\[ \frac{405 \div 45}{225 \div 45} = \frac{9}{5} = 1.8 \]

### Conclusion
Thus, the value of the expression is:
\[ \frac{9}{2} = 4.5 \]