Evaluate the product 3 × 0.3 × 0.03 × 0.003 × 30 and choose the correct decimal value.

Introduction / Context:
This problem checks your fluency with multiplication of decimals and understanding of how place values shift when you multiply several decimal numbers together. Such questions appear frequently in decimal fractions and number system sections of aptitude tests and are designed to test both calculation accuracy and place value concepts.

Given Data / Assumptions:

• The numbers to be multiplied are 3, 0.3, 0.03, 0.003, and 30.
• All values are real numbers, and the operations are simple multiplication.
• We have to compute the exact decimal product and match it with one of the given options.
• No rounding is required because the options are given with precise decimal digits.

Concept / Approach:
The key concept is that multiplying by 10, 100, and so on shifts the decimal point to the right, while multiplying by tenths, hundredths, or thousandths shifts it to the left. A helpful strategy is to separate the calculation into a product of whole numbers and a power of 10 derived from counting decimal places. Alternatively, you can multiply step by step while being very careful with decimal positions.

Step-by-Step Solution:
First group the whole number factors: 3 × 30 = 90.Next, multiply the decimal factors: 0.3 × 0.03 × 0.003.Write them as powers of 10: 0.3 = 3 × 10^-1, 0.03 = 3 × 10^-2, 0.003 = 3 × 10^-3.Then 0.3 × 0.03 × 0.003 = (3 × 3 × 3) × 10^(-1-2-3) = 27 × 10^-6.Now multiply this with 90: 90 × 27 × 10^-6.Compute 90 × 27 = 2430.So the overall product is 2430 × 10^-6 = 0.00243.Therefore, the required value is 0.00243.

Verification / Alternative check:
As a quick check, you can multiply directly on a calculator or carefully by hand: 3 × 0.3 = 0.9, 0.9 × 0.03 = 0.027, 0.027 × 0.003 = 0.000081, and 0.000081 × 30 = 0.00243. Both methods produce the same answer, confirming that our place value handling is correct and that no decimal has been misplaced.

Why Other Options Are Wrong:
Option 0.0000243 is smaller by a factor of 100 and would result from shifting the decimal two places too far to the left. Option 0.000243 is smaller by a factor of 10, indicating one extra left shift. Option 0.0243 is larger by a factor of 10, suggesting one fewer left shift. Option 0.00000243 is off by a factor of 1000 and reflects an even more serious mistake with powers of 10.

Common Pitfalls:
Learners often miscount the total number of decimal places and shift the decimal incorrectly. Another common mistake is to ignore that both 3 and 30 are whole numbers, so they do not contribute additional decimal places. Some may multiply 0.3, 0.03, and 0.003 incorrectly due to confusion about tenths, hundredths, and thousandths. Careful writing of intermediate steps and use of scientific notation are effective ways to avoid these errors.

Final Answer:
The value of 3 × 0.3 × 0.03 × 0.003 × 30 is 0.00243.