What approximate value will come in place of question mark (?) in the following questions? (You are not excepted to calculate the exact value.)
`(1/(24.99xx32.12)-1/(32.12))xx(406.103-2xx3)=?`

Options

A. `-36`
B. `-72`
C. 12
D. `-12`

Answer

To solve the expression `(1/(24.99 * 32.12) - 1/(32.12)) * (406.103 - 2 * 3) = ?`, we will approximate the values step by step.

### Step 1: Approximate the values
- We can approximate `24.99` to `25` and `32.12` to `32` for easier calculations.

### Step 2: Rewrite the expression
- The expression becomes:
\[ \left( \frac{1}{25 \times 32} - \frac{1}{32} \right) \times (406.103 - 6) \]

### Step 3: Simplify the first part
- Calculate \( 25 \times 32 \):
\[ 25 \times 32 = 800 \]
- So, \( \frac{1}{25 \times 32} \) becomes \( \frac{1}{800} \).
- The expression now looks like:
\[ \left( \frac{1}{800} - \frac{1}{32} \right) \times (406.103 - 6) \]

### Step 4: Find a common denominator
- The common denominator for \( 800 \) and \( 32 \) is \( 800 \).
- Rewrite \( \frac{1}{32} \) as \( \frac{25}{800} \):
\[ \frac{1}{800} - \frac{25}{800} = \frac{1 - 25}{800} = \frac{-24}{800} \]

### Step 5: Simplify the fraction
- Simplifying \( \frac{-24}{800} \):
\[ \frac{-24}{800} = \frac{-3}{100} = -0.03 \]

### Step 6: Calculate the second part
- Now calculate \( 406.103 - 6 \):
\[ 406.103 - 6 = 400.103 \approx 400 \]

### Step 7: Combine the results
- Now we multiply:
\[ \left( -0.03 \right) \times 400 = -12 \]

### Final Result
- Therefore, the approximate value that comes in place of the question mark (?) is:
\[ \boxed{-12} \]