Sure! Let's solve the given problem step-by-step.
### Step 1: Find the Reciprocal of 0.325
The reciprocal of a number [tex]\( x \)[/tex] is given by [tex]\( \frac{1}{x} \)[/tex].
For [tex]\( x = 0.325 \)[/tex]:
[tex]\[
0.325^{-1} = \frac{1}{0.325} \approx 3.0769
\][/tex]
So the reciprocal of 0.325 is approximately 3.0769.
### Step 2: Evaluate [tex]\(\sqrt{0.0000125}\)[/tex]
We need to calculate the square root of 0.0000125.
[tex]\[
\sqrt{0.0000125} \approx 0.0035355
\][/tex]
### Step 3: Substitute Values Into the Expression
Now, we substitute the values we have into the expression [tex]\(\left(\frac{3 \sqrt{0.0000125}}{0.325}\right)\)[/tex]:
[tex]\[
\left(\frac{3 \times 0.0035355}{0.325}\right)
\][/tex]
### Step 4: Simplify the Expression
First, multiply the number inside the parentheses:
[tex]\[
3 \times 0.0035355 = 0.0106065
\][/tex]
Then, divide by 0.325:
[tex]\[
\frac{0.0106065}{0.325} \approx 0.0326357
\][/tex]
### Step 5: Round the Result to 4 Significant Figures
Finally, we round the result to 4 significant figures:
[tex]\[
0.0326357 \approx 0.03264
\][/tex]
### Answer
Thus, the value of [tex]\( (0.325)^{-1} \)[/tex] is approximately [tex]\( 3.0769 \)[/tex], and the value of [tex]\(\left(\frac{3 \sqrt{0.0000125}}{0.325}\right) \)[/tex] to 4 significant figures is approximately [tex]\( 0.03264 \)[/tex].
