Answer :
Sure! Let's work through these conversions step by step using dimensional analysis.
### Part 1: Convert 0.189 mg to kg
Dimensional analysis involves using conversion factors to move from one unit to another. We know that:
1,000,000 milligrams (mg) = 1 kilogram (kg)
or equivalently [tex]\( 1 \text{ mg} = 1 \times 10^{-6} \text{ kg} \)[/tex].
So, to convert 0.189 mg to kg, you can set up the conversion factor as follows:
[tex]\[
0.189 \text{ mg} \times \left(\frac{1 \text{ kg}}{1,000,000 \text{ mg}}\right) = 0.189 \times 10^{-6} \text{ kg} = 1.89 \times 10^{-7} \text{ kg}
\][/tex]
This means that 0.189 mg is equal to [tex]\(1.89 \times 10^{-7} \text{ kg}\)[/tex].
### Part 2: Convert 116 kg to mg
Again, using dimensional analysis, we know that:
1 kilogram (kg) = 1,000,000 milligrams (mg).
To convert 116 kg to mg, you set up the conversion factor as follows:
[tex]\[
116 \text{ kg} \times \left(\frac{1,000,000 \text{ mg}}{1 \text{ kg}}\right) = 116 \times 1,000,000 \text{ mg} = 116,000,000 \text{ mg}
\][/tex]
Thus, 116 kg is equal to 116,000,000 mg.
These conversions show how you can use dimensional analysis to convert units accurately!
### Part 1: Convert 0.189 mg to kg
Dimensional analysis involves using conversion factors to move from one unit to another. We know that:
1,000,000 milligrams (mg) = 1 kilogram (kg)
or equivalently [tex]\( 1 \text{ mg} = 1 \times 10^{-6} \text{ kg} \)[/tex].
So, to convert 0.189 mg to kg, you can set up the conversion factor as follows:
[tex]\[
0.189 \text{ mg} \times \left(\frac{1 \text{ kg}}{1,000,000 \text{ mg}}\right) = 0.189 \times 10^{-6} \text{ kg} = 1.89 \times 10^{-7} \text{ kg}
\][/tex]
This means that 0.189 mg is equal to [tex]\(1.89 \times 10^{-7} \text{ kg}\)[/tex].
### Part 2: Convert 116 kg to mg
Again, using dimensional analysis, we know that:
1 kilogram (kg) = 1,000,000 milligrams (mg).
To convert 116 kg to mg, you set up the conversion factor as follows:
[tex]\[
116 \text{ kg} \times \left(\frac{1,000,000 \text{ mg}}{1 \text{ kg}}\right) = 116 \times 1,000,000 \text{ mg} = 116,000,000 \text{ mg}
\][/tex]
Thus, 116 kg is equal to 116,000,000 mg.
These conversions show how you can use dimensional analysis to convert units accurately!
