To solve the problem, we need to multiply \(-1.7%\) by \(2 \frac{1}{2}%\).
First, let's convert both percentages to fractions:
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Convert \(-1.7%\) to a fraction: \[ -1.7% = -\frac{1.7}{100} = -\frac{17}{1000} \]
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Convert \(2 \frac{1}{2}%\) to a fraction: \[ 2 \frac{1}{2}% = \left(2 + \frac{1}{2}\right)% = \frac{5}{2}% \] \[ \frac{5}{2}% = \frac{5}{2} \times \frac{1}{100} = \frac{5}{200} = \frac{1}{40} \]
Now we can multiply the two fractions: \[ \text{Multiplication: } -\frac{17}{1000} \times \frac{1}{40} = -\frac{17 \times 1}{1000 \times 40} \] Calculating the denominator: \[ 1000 \times 40 = 40000 \]
Then, the multiplication becomes: \[ -\frac{17}{40000} \]
Next, we will write \(-\frac{17}{40000}\) as a mixed number. Since the numerator \(17\) is less than \(40000\), the whole number part is \(0\), and we will focus on the fractional part: \[ -\frac{17}{40000} \]
Now, we need to simplify \(\frac{17}{40000}\):
- \(17\) is a prime number, and \(40000\) can be factored into \(2^8 \times 5^4\), so there are no common factors to simplify further.
Thus, the simplest form of the fraction is \(-\frac{17}{40000}\).
Since there is no whole number part, the answer as a mixed number is: \[ 0 - \frac{17}{40000} = -\frac{17}{40000} \]
The answer as a mixed number in simplest form is: \[ -\frac{17}{40000} \]
(Note: No available option in your list matches \(-\frac{17}{40000}\), so verify the available options, as they seem incorrect.)