Simplify: `(0.00081)/(0.09)`

Answer

To simplify the expression \((0.00081)/(0.09)\), we can follow these steps:

### Step 1: Rewrite the numbers in scientific notation
We can express \(0.00081\) and \(0.09\) in scientific notation:
- \(0.00081 = 81 \times 10^{-5}\)
- \(0.09 = 9 \times 10^{-2}\)

### Step 2: Set up the division
Now we can rewrite the division:
\[ \frac{0.00081}{0.09} = \frac{81 \times 10^{-5}}{9 \times 10^{-2}} \]

### Step 3: Simplify the fraction
We can simplify the fraction by dividing the coefficients and subtracting the exponents:
\[ \frac{81}{9} = 9 \]
For the powers of ten:
\[ 10^{-5} \div 10^{-2} = 10^{-5 - (-2)} = 10^{-5 + 2} = 10^{-3} \]

### Step 4: Combine the results
Now we can combine the results from the previous step:
\[ \frac{0.00081}{0.09} = 9 \times 10^{-3} \]

### Step 5: Convert back to decimal form
To convert \(9 \times 10^{-3}\) back to decimal form:
\[ 9 \times 10^{-3} = \frac{9}{1000} = 0.009 \]

### Final Answer
Thus, the simplified form of \((0.00081)/(0.09)\) is:
\[ \boxed{0.009} \]

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