To identify which scientific notation correctly represents the number 2,417, let's evaluate each given option:
### Option 1: [tex]\( 2.417 \times 10^{-3} \)[/tex]
Evaluating this:
[tex]\[ 2.417 \times 10^{-3} = 2.417 \times 0.001 = 0.002417 \][/tex]
This is clearly not equal to 2,417.
### Option 2: [tex]\( 2.417 \times 10^3 \)[/tex]
Evaluating this:
[tex]\[ 2.417 \times 10^3 = 2.417 \times 1000 = 2417 \][/tex]
This matches the number we are trying to represent, which is 2,417.
### Option 3: [tex]\( 24.17 \times 10^3 \)[/tex]
Evaluating this:
[tex]\[ 24.17 \times 10^3 = 24.17 \times 1000 = 24170 \][/tex]
This is not equal to 2,417; it's ten times larger.
### Option 4: [tex]\( 2.417 \times 10^4 \)[/tex]
Evaluating this:
[tex]\[ 2.417 \times 10^4 = 2.417 \times 10000 = 24170 \][/tex]
This also does not match 2,417; it is again ten times larger.
Given the evaluations:
- Option 1 resulted in 0.002417.
- Option 3 resulted in 24,170.
- Option 4 resulted in 24,170.
Clearly, only Option 2, [tex]\( 2.417 \times 10^3 \)[/tex], correctly corresponds to the number 2,417. Therefore, the correct option is:
[tex]\[ \boxed{2} \][/tex]
