Solving for 3 Times 3 Tenths of 3 Hundredths of 3 Thousandths of 30

The problem asks us to calculate the value of a series of multiplications involving fractions and a base number. We need to find "3 times of 3 tenths of 3 hundredths of 3 thousandths of 30".

Mathematical Expression Setup

First, let's convert the fractions into mathematical terms:

• 3 tenths = $\frac{3}{10}$
• 3 hundredths = $\frac{3}{100}$
• 3 thousandths = $\frac{3}{1000}$

The phrase "A of B" means $A \times B$. Therefore, the entire expression can be written as:

$3 \times \frac{3}{10} \times \frac{3}{100} \times \frac{3}{1000} \times 30$

Step-by-Step Calculation

Let's calculate the value step-by-step:

1. Combine the numerical parts and the fractional parts: $(3 \times 3 \times 3 \times 3 \times 30) \times (\frac{1}{10} \times \frac{1}{100} \times \frac{1}{1000})$
2. Calculate the product of the numerators: $3 \times 3 \times 3 \times 3 = 81$ $81 \times 30 = 2430$
3. Calculate the product of the denominators: $10 \times 100 \times 1000 = 1,000,000$
4. Combine the results: $\frac{2430}{1,000,000}$
5. Convert the fraction to a decimal: $0.002430$ which simplifies to $0.00243$.

Final Result

The value of 3 times of 3 tenths of 3 hundredths of 3 thousandths of 30 is $0.00243$.