To convert 0.329 kilograms (kg) into milligrams (mg), follow these detailed steps:
1. Understand the Conversion Factor:
1 kilogram (kg) is equal to 1,000,000 milligrams (mg).
2. Perform the Conversion:
To find the number of milligrams in 0.329 kilograms, you multiply the mass in kilograms by the conversion factor.
[tex]\[
0.329 \, \text{kg} \times 1,000,000 \, \text{mg/kg} = 329,000 \, \text{mg}
\][/tex]
3. Express the Result in Scientific Notation:
Scientific notation represents numbers as the product of a coefficient and a power of 10. For 329,000 milligrams:
[tex]\[
329,000 = 3.29 \times 10^5 \, \text{mg}
\][/tex]
4. Adjust to the Given Format:
However, you need to convert it to the format that specifies a coefficient where you're shifting the decimal point to significant figures:
Here, it would be:
[tex]\[
329,000 = 329 \times 10^3 \, \text{mg}
\][/tex]
Therefore, the conversion from 0.329 kilograms to milligrams in scientific notation can be given as:
Coefficient (green): [tex]\( \boxed{329} \)[/tex]
Exponent (yellow): [tex]\( \boxed{3} \)[/tex]
So, [tex]\(0.329 \, \text{kg} = 329 \times 10^3 \, \text{mg}\)[/tex].
