The value of `(3.157 xx 4126 xx 3. 198)/(63.972 xx 2835.212)` is closest to

Options

A. `0.002`
B. `0.002`
C. `0.2`
D. `2`

Answer

To solve the expression \((3.157 \times 4126 \times 3.198) / (63.972 \times 2835.212)\) and find its approximate value, we can follow these steps:

### Step 1: Approximate each number
- **3.157** can be approximated to **3** (since 0.157 is small).
- **4126** remains **4126** (as it is already a whole number).
- **3.198** can be approximated to **3.2** (since it is close to 3.2).
- **63.972** can be approximated to **64** (as it is very close to 64).
- **2835.212** can be approximated to **2835** (as the decimal part is small).

### Step 2: Rewrite the expression with approximated values
Now, we can rewrite the expression with the approximated values:
\[ \frac{(3 \times 4126 \times 3.2)}{(64 \times 2835)} \]

### Step 3: Simplify the expression
First, calculate the numerator:
\[ 3 \times 4126 \times 3.2 \]
Calculating \(3 \times 4126 = 12378\),
Then, \(12378 \times 3.2 = 39597.6\).

Next, calculate the denominator:
\[ 64 \times 2835 = 181440 \]

### Step 4: Divide the simplified numerator by the denominator
Now we can divide:
\[ \frac{39597.6}{181440} \]

### Step 5: Estimate the division
To estimate this division, we can simplify:
\[ \frac{39597.6}{181440} \approx \frac{40000}{180000} = \frac{4}{18} = \frac{2}{9} \approx 0.222 \]

### Step 6: Round the result
Rounding \(0.222\) gives us approximately **0.2**.

### Conclusion
Thus, the value of the expression \((3.157 \times 4126 \times 3.198) / (63.972 \times 2835.212)\) is closest to **0.2**.

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