Institution: Directorate of Primary Education - DPE Exam: Primary Exam Question Solution 21-06-2019
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the multiplication problem \(0.4 \times 0.02 \times 0.08\), we need to understand how to multiply decimals and how significant figures relate to this process.

First, we can break the calculation down step-by-step:

1. Start by multiplying the first two numbers: \(0.4 \times 0.02\).
- \(0.4\) can be expressed as \(4 \times 10^{-1}\) (which means 4 tenths), and \(0.02\) as \(2 \times 10^{-2}\).
- Multiplying these gives:
\[
4 \times 2 = 8 \quad \text{and} \quad 10^{-1} \times 10^{-2} = 10^{-3}
\]
- So, \(0.4 \times 0.02 = 8 \times 10^{-3} = 0.008\).

2. Next, take the result \(0.008\) and multiply it by \(0.08\).
- Here, \(0.08\) can be expressed as \(8 \times 10^{-2}\).
- Now perform the multiplication:
\[
0.008 \times 0.08 = (8 \times 10^{-3}) \times (8 \times 10^{-2}) = 64 \times 10^{-5} = 0.00064.
\]

Finally, as we follow the multiplication of decimals, we can confirm that there were a total of 6 decimal places (1 from \(0.4\), 2 from \(0.02\), and 2 from \(0.08\)). Therefore, the result of this multiplication is indeed \(0.00064\), making the correct answer option A: \(0.00064\).