To determine which number is equivalent to [tex]\(3.82 \times 10^{-5}\)[/tex], let's examine and compare each given number.
### Step-by-Step Analysis
#### Step 1: Understanding the Scientific Notation
First, interpret the expression [tex]\(3.82 \times 10^{-5}\)[/tex]:
- The base is 3.82.
- The exponent is [tex]\(-5\)[/tex], which means we move the decimal point 5 places to the left.
#### Step 2: Convert [tex]\(3.82 \times 10^{-5}\)[/tex] to Standard Notation
Move the decimal point 5 places to the left:
[tex]\[ 3.82 \rightarrow 0.0000382 \][/tex]
So, [tex]\(3.82 \times 10^{-5} = 0.0000382\)[/tex].
#### Step 3: Compare with Given Options
Now, compare [tex]\(0.0000382\)[/tex] with each option provided:
1. 382,000: This is much larger than [tex]\(0.0000382\)[/tex].
2. 0.0000382: This matches exactly what we calculated.
3. [tex]\(-191\)[/tex]: This is a negative value and does not match [tex]\(0.0000382\)[/tex].
4. 19.1: This is much larger than [tex]\(0.0000382\)[/tex].
After comparison, we see that the value [tex]\(0.0000382\)[/tex] is the correct match.
Therefore, the number equivalent to [tex]\(3.82 \times 10^{-5}\)[/tex] is:
[tex]\[ \boxed{0.0000382} \][/tex]
