Find the value of `200 xx 20 xx 2 xx 0.2 xx 0.02xx 0.002=` ?
A. 0.064
B 0.64
C. 64
D 640

Options

A. C
B. A
C. D
D. B

Answer

To solve the expression \(200 \times 20 \times 2 \times 0.2 \times 0.02 \times 0.002\), we can break it down step by step.

### Step 1: Rewrite the numbers in scientific notation
We can express each number in the product in terms of powers of 10:
- \(200 = 2 \times 10^2\)
- \(20 = 2 \times 10^1\)
- \(2 = 2 \times 10^0\)
- \(0.2 = 2 \times 10^{-1}\)
- \(0.02 = 2 \times 10^{-2}\)
- \(0.002 = 2 \times 10^{-3}\)

### Step 2: Combine the factors
Now we can rewrite the expression using these representations:
\[ (2 \times 10^2) \times (2 \times 10^1) \times (2 \times 10^0) \times (2 \times 10^{-1}) \times (2 \times 10^{-2}) \times (2 \times 10^{-3}) \]

### Step 3: Group the constants and powers of 10
Now we can group all the \(2\)s and all the \(10\)s:
- The constant part: \(2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64\)
- The power of 10: \(10^{2 + 1 + 0 - 1 - 2 - 3}\)

### Step 4: Calculate the exponent for powers of 10
Calculating the exponent:
\[ 2 + 1 + 0 - 1 - 2 - 3 = 2 + 1 - 1 - 2 - 3 = -3 \]
So we have \(10^{-3}\).

### Step 5: Combine the results
Now we combine the results:
\[ 64 \times 10^{-3} = 64 \times \frac{1}{1000} = \frac{64}{1000} = 0.064 \]

### Final Answer
Thus, the value of \(200 \times 20 \times 2 \times 0.2 \times 0.02 \times 0.002\) is \(0.064\).