`{:("Column A"," ","Column B"),(2 xx 10^1 + 3 xx 10^(0) +4 xx 10^(-1) + 5 xx 10^(-2),,1 xx 10^(-3) + 2 xx 10^(-2) xx 10^(-2) + 3 xx 10^(-1) + 4 xx 10^(0) + 5 xx 10^(1)):}`

Options

A. If column A is larger
B. If column B is larger
C. If the columns are equal
D. If there is not enough information to decide

Answer

To solve the problem, we need to evaluate the expressions in Column A and Column B separately and then compare their values.

### Step 1: Evaluate Column A
The expression for Column A is:
\[ 2 \times 10^1 + 3 \times 10^0 + 4 \times 10^{-1} + 5 \times 10^{-2} \]

1. **Calculate each term:**
- \( 2 \times 10^1 = 20 \)
- \( 3 \times 10^0 = 3 \) (since \( 10^0 = 1 \))
- \( 4 \times 10^{-1} = \frac{4}{10} = 0.4 \)
- \( 5 \times 10^{-2} = \frac{5}{100} = 0.05 \)

2. **Add the terms together:**
\[ 20 + 3 + 0.4 + 0.05 = 23.45 \]

### Step 2: Evaluate Column B
The expression for Column B is:
\[ 1 \times 10^{-3} + 2 \times 10^{-2} \times 10^{-2} + 3 \times 10^{-1} + 4 \times 10^0 + 5 \times 10^1 \]

1. **Calculate each term:**
- \( 1 \times 10^{-3} = \frac{1}{1000} = 0.001 \)
- \( 2 \times 10^{-2} \times 10^{-2} = 2 \times 10^{-4} = \frac{2}{10000} = 0.0002 \)
- \( 3 \times 10^{-1} = \frac{3}{10} = 0.3 \)
- \( 4 \times 10^0 = 4 \)
- \( 5 \times 10^1 = 50 \)

2. **Add the terms together:**
\[ 0.001 + 0.0002 + 0.3 + 4 + 50 = 54.3012 \]

### Step 3: Compare Column A and Column B
Now we have:
- Column A = 23.45
- Column B = 54.3012

Since \( 54.3012 > 23.45 \), we conclude that Column B is larger.

### Final Conclusion
The value of Column B is greater than the value of Column A.

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