`3.0xx0.3xx0.03xx0.003=?`

Options

A. `81xx10^(-4)`
B. `81xx10^(-7)`
C. `81xx10^(-5)`
D. `81xx10^(-6)`

Answer

To solve the expression \(3.0 \times 0.3 \times 0.03 \times 0.003\), we will follow these steps:

### Step 1: Convert the decimal numbers into fractions
We can express each decimal number as a fraction:
- \(3.0 = \frac{3}{1}\)
- \(0.3 = \frac{3}{10}\)
- \(0.03 = \frac{3}{100}\)
- \(0.003 = \frac{3}{1000}\)

### Step 2: Write the expression as a product of fractions
Now, we can rewrite the expression:
\[ 3.0 \times 0.3 \times 0.03 \times 0.003 = \frac{3}{1} \times \frac{3}{10} \times \frac{3}{100} \times \frac{3}{1000} \]

### Step 3: Multiply the numerators and denominators
Multiply all the numerators together and all the denominators together:
\[ \text{Numerator: } 3 \times 3 \times 3 \times 3 = 3^4 \]
\[ \text{Denominator: } 1 \times 10 \times 100 \times 1000 = 10^{1+2+3} = 10^6 \]

### Step 4: Simplify the expression
Now we can simplify the expression:
\[ \frac{3^4}{10^6} \]

### Step 5: Calculate \(3^4\)
Now we calculate \(3^4\):
\[ 3^4 = 3 \times 3 \times 3 \times 3 = 9 \times 3 = 27 \times 3 = 81 \]

### Step 6: Write the final answer
Thus, we have:
\[ \frac{81}{10^6} \]
This can also be written in decimal form as:
\[ 0.000081 \]

### Conclusion
The final answer is:
\[ 0.000081 \]

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