`12div0.09of 0.3xx2=?`

Options

A. 0.8
B. 0.08
C. 8
D. none of these

Answer

To solve the expression \( 12 \div 0.09 \text{ of } 0.3 \times 2 \), we will follow the order of operations (BODMAS/BIDMAS). Here’s a step-by-step breakdown:

### Step 1: Understand the Expression
The expression can be rewritten as:
\[ 12 \div (0.09 \times 0.3 \times 2) \]

### Step 2: Calculate \( 0.3 \times 2 \)
First, we will multiply \( 0.3 \) and \( 2 \):
\[ 0.3 \times 2 = 0.6 \]

**Hint:** Remember that multiplying a decimal by a whole number shifts the decimal point based on the number of digits in the whole number.

### Step 3: Calculate \( 0.09 \times 0.6 \)
Next, we will multiply \( 0.09 \) by \( 0.6 \):
\[ 0.09 \times 0.6 = 0.054 \]

**Hint:** When multiplying decimals, count the total number of decimal places in both numbers to place the decimal point correctly in the result.

### Step 4: Divide \( 12 \) by \( 0.054 \)
Now we will divide \( 12 \) by \( 0.054 \):
\[ 12 \div 0.054 \]

To perform this division, we can convert \( 0.054 \) to a fraction:
\[ 0.054 = \frac{54}{1000} \]
Thus,
\[ 12 \div 0.054 = 12 \times \frac{1000}{54} \]

**Hint:** Dividing by a decimal can be simplified by converting it into a fraction, which can make calculations easier.

### Step 5: Simplify the Expression
Now we simplify:
\[ 12 \times \frac{1000}{54} = \frac{12000}{54} \]

### Step 6: Reduce the Fraction
Now, we can simplify \( \frac{12000}{54} \):
\[ \frac{12000 \div 6}{54 \div 6} = \frac{2000}{9} \]

**Hint:** Always look for common factors to simplify fractions.

### Step 7: Calculate the Final Result
Now, we can convert \( \frac{2000}{9} \) into a decimal:
\[ 2000 \div 9 \approx 222.22 \]

Thus, the final answer is:
\[ \boxed{222.22} \]

### Summary of Steps:
1. Rewrite the expression.
2. Multiply \( 0.3 \) and \( 2 \).
3. Multiply \( 0.09 \) and the result from step 2.
4. Divide \( 12 \) by the result from step 3.
5. Simplify the fraction.
6. Convert the final fraction to a decimal.