To determine which choices are written correctly in scientific notation, let's review the rules for scientific notation.
A number is in scientific notation if it is written in the form:
[tex]\[ a \times 10^b \][/tex]
where:
- [tex]\( a \)[/tex] is a number greater than or equal to 1 and less than 10 (1 <= a < 10),
- [tex]\( b \)[/tex] is an integer (can be positive, negative, or zero).
Now, let's analyze each of the given choices:
1. [tex]\( 17.1 \times 10^2 \)[/tex]:
- The coefficient [tex]\( 17.1 \)[/tex] is not between 1 and 10. Hence, this is not correct scientific notation.
2. [tex]\( 8.05 \times 10^2 \)[/tex]:
- The coefficient [tex]\( 8.05 \)[/tex] is between 1 and 10.
- The base is [tex]\( 10 \)[/tex].
- The exponent [tex]\( 2 \)[/tex] is an integer.
- This notation is correct.
3. [tex]\( 0.25 \times 44^2 \)[/tex]:
- The coefficient [tex]\( 0.25 \)[/tex] is not between 1 and 10.
- The base is [tex]\( 44 \)[/tex], not [tex]\( 10 \)[/tex].
- This notation is not correct.
4. [tex]\( 4 \times 10^{-10} \)[/tex]:
- The coefficient [tex]\( 4 \)[/tex] is between 1 and 10.
- The base is [tex]\( 10 \)[/tex].
- The exponent [tex]\( -10 \)[/tex] is an integer.
- This notation is correct.
5. [tex]\( 22 \text{ an} \times 10+ \)[/tex]:
- The coefficient [tex]\( 22 \text{ an} \)[/tex] is not a numerical value.
- The base is not clearly defined as 10.
- This notation is incorrect.
6. [tex]\( 3.03 \times 10^{-1} \)[/tex]:
- The coefficient [tex]\( 3.03 \)[/tex] is between 1 and 10.
- The base is [tex]\( 10 \)[/tex].
- The exponent [tex]\( -1 \)[/tex] is an integer.
- This notation is correct.
7. Ex. 4010:
- This is simply a number, not written in the form [tex]\( a \times 10^b \)[/tex].
- This notation is incorrect.
8. [tex]\( 344 \times 1^{10} \)[/tex]:
- The coefficient [tex]\( 344 \)[/tex] is not between 1 and 10.
- The base [tex]\( 1 \)[/tex] is not 10.
- This notation is incorrect.
From this analysis, the choices that are correctly written in scientific notation are:
[tex]\[ 8.05 \times 10^2 \][/tex]
[tex]\[ 4 \times 10^{-10} \][/tex]
[tex]\[ 3.03 \times 10^{-1} \][/tex]
These three choices are the correct ones based on the rules for scientific notation. However, the question is asking for four correct answers. Since we only found three valid answers, there may have been an error in the question or some additional, context-specific criteria that we aren't aware of. Nonetheless, the three identified choices are certainly correct in standard scientific notation.
