Find the product `0.47 x 5.3 x 0.06`

Answer

To find the product of \(0.47 \times 5.3 \times 0.06\), we can follow these steps:

### Step 1: Remove the Decimals
First, we will convert the decimal numbers into fractions to make multiplication easier.

- For \(0.47\): Since there are 2 digits after the decimal, we can express it as:
\[ 0.47 = \frac{47}{100} \]

- For \(5.3\): Since there is 1 digit after the decimal, we can express it as:
\[ 5.3 = \frac{53}{10} \]

- For \(0.06\): Since there are 2 digits after the decimal, we can express it as:
\[ 0.06 = \frac{6}{100} \]

### Step 2: Multiply the Fractions
Now we can multiply these fractions together:
\[ 0.47 \times 5.3 \times 0.06 = \frac{47}{100} \times \frac{53}{10} \times \frac{6}{100} \]

### Step 3: Multiply the Numerators and Denominators
Next, we multiply the numerators and the denominators:
\[ \text{Numerator: } 47 \times 53 \times 6 \]
\[ \text{Denominator: } 100 \times 10 \times 100 = 100000 \]

Calculating the numerator:
1. First, calculate \(47 \times 53\):
\[ 47 \times 53 = 2491 \]
2. Then, multiply the result by \(6\):
\[ 2491 \times 6 = 14946 \]

So, the numerator is \(14946\).

### Step 4: Combine the Results
Now we can write the product as:
\[ \frac{14946}{100000} \]

### Step 5: Convert Back to Decimal
To convert the fraction back to decimal, we divide:
\[ 14946 \div 100000 = 0.14946 \]

### Final Answer
Thus, the product \(0.47 \times 5.3 \times 0.06\) is:
\[ \boxed{0.14946} \]

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