To convert centigrams (cg) to kilograms (kg) and express the result in scientific notation, follow these steps:
1. Understand the conversion factors:
- [tex]\(1 \text{ centigram (cg)} = 10^{-2} \text{ grams (g)}\)[/tex]
- [tex]\(1 \text{ gram (g)} = 10^{-3} \text{ kilograms (kg)}\)[/tex]
2. Convert centigrams to grams:
- We start with 865 centigrams.
- Since 1 centigram = [tex]\(10^{-2}\)[/tex] grams, 865 centigrams can be converted to grams by multiplying by [tex]\(10^{-2}\)[/tex]:
[tex]\[
865 \text{ cg} = 865 \times 10^{-2} \text{ g} = 8.65 \text{ g}
\][/tex]
3. Convert grams to kilograms:
- Now, convert 8.65 grams to kilograms.
- Since 1 gram = [tex]\(10^{-3}\)[/tex] kilograms, we multiply 8.65 grams by [tex]\(10^{-3}\)[/tex]:
[tex]\[
8.65 \text{ g} = 8.65 \times 10^{-3} \text{ kg} = 0.00865 \text{ kg}
\][/tex]
4. Express the result in scientific notation:
- To express 0.00865 kg in scientific notation, identify the coefficient and the exponent.
- Move the decimal point 3 places to the right, which means multiplying by [tex]\(10^{-3}\)[/tex]:
[tex]\[
0.00865 \text{ kg} = 8.65 \times 10^{-3} \text{ kg}
\][/tex]
Therefore, the coefficient (green) is:
[tex]\[
\boxed{8.65}
\][/tex]
And the exponent (yellow) is:
[tex]\[
\boxed{-3}
\][/tex]
