Let's convert 865 centigrams (cg) to kilograms (kg) step by step and express the result in scientific notation.
1. Convert Centigrams to Grams:
- We know that [tex]\( 1 \)[/tex] centigram is equal to [tex]\( 10^{-2} \)[/tex] grams.
- Therefore, [tex]\( 865 \)[/tex] centigrams can be converted to grams as follows:
[tex]\[
865 \, \text{cg} = 865 \times 10^{-2} \, \text{g} = 8.65 \, \text{g}
\][/tex]
2. Convert Grams to Kilograms:
- We know that [tex]\( 1 \)[/tex] gram is equal to [tex]\( 10^{-3} \)[/tex] kilograms.
- Therefore, [tex]\( 8.65 \)[/tex] grams can be converted to kilograms as follows:
[tex]\[
8.65 \, \text{g} = 8.65 \times 10^{-3} \, \text{kg}
\][/tex]
3. Expressing in Scientific Notation:
- Scientific notation requires expressing the number in the form of [tex]\( a \times 10^b \)[/tex], where [tex]\( 1 \leq a < 10 \)[/tex].
- Here, we already have [tex]\( 8.65 \times 10^{-3} \)[/tex].
- The coefficient [tex]\( a \)[/tex] is [tex]\( 8.65 \)[/tex], and the exponent [tex]\( b \)[/tex] is [tex]\( -3 \)[/tex].
Therefore, [tex]\( 865 \)[/tex] centigrams can be expressed as:
[tex]\[
\boxed{8.65} \times 10^{\boxed{-3}} \, \text{kg}
\][/tex]
So, the final coefficient is [tex]\(\boxed{8.65}\)[/tex] and the exponent is [tex]\(\boxed{-3}\)[/tex].
