Let's work on converting the given measurements step-by-step.
### Part a: Express 35 mm in cm, m, and km.
We will convert 35 millimeters (mm) into centimeters (cm), meters (m), and kilometers (km).
1. Convert millimeters to centimeters:
- We know that [tex]\( 1 \)[/tex] centimeter (cm) is equal to [tex]\( 10 \)[/tex] millimeters (mm).
- To convert millimeters to centimeters, we divide by [tex]\( 10 \)[/tex].
- So, [tex]\( 35 \)[/tex] millimeters (mm) is equal to [tex]\( \frac{35}{10} \)[/tex] centimeters (cm).
Therefore,
[tex]\( 35 \)[/tex] mm = [tex]\( 3.5 \)[/tex] cm.
2. Convert millimeters to meters:
- We know that [tex]\( 1 \)[/tex] meter (m) is equal to [tex]\( 1000 \)[/tex] millimeters (mm).
- To convert millimeters to meters, we divide by [tex]\( 1000 \)[/tex].
- So, [tex]\( 35 \)[/tex] millimeters (mm) is equal to [tex]\( \frac{35}{1000} \)[/tex] meters (m).
Therefore,
[tex]\( 35 \)[/tex] mm = [tex]\( 0.035 \)[/tex] m.
3. Convert millimeters to kilometers:
- We know that [tex]\( 1 \)[/tex] kilometer (km) is equal to [tex]\( 1,000,000 \)[/tex] millimeters (mm).
- To convert millimeters to kilometers, we divide by [tex]\( 1,000,000 \)[/tex].
- So, [tex]\( 35 \)[/tex] millimeters (mm) is equal to [tex]\( \frac{35}{1,000,000} \)[/tex] kilometers (km).
Therefore,
[tex]\( 35 \)[/tex] mm = [tex]\( 3.5 \times 10^{-5} \)[/tex] km or [tex]\( 3.5e-05 \)[/tex] km.
### Part b: Express 200 g in kg.
We will convert 200 grams (g) into kilograms (kg).
1. Convert grams to kilograms:
- We know that [tex]\( 1 \)[/tex] kilogram (kg) is equal to [tex]\( 1000 \)[/tex] grams (g).
- To convert grams to kilograms, we divide by [tex]\( 1000 \)[/tex].
- So, [tex]\( 200 \)[/tex] grams (g) is equal to [tex]\( \frac{200}{1000} \)[/tex] kilograms (kg).
Therefore,
[tex]\( 200 \)[/tex] g = [tex]\( 0.2 \)[/tex] kg.
### Summary of Conversions:
a. [tex]\( 35 \)[/tex] mm = [tex]\( 3.5 \)[/tex] cm, [tex]\( 0.035 \)[/tex] m, [tex]\( 3.5 \times 10^{-5} \)[/tex] km or [tex]\( 3.5e-05 \)[/tex] km.
b. [tex]\( 200 \)[/tex] g = [tex]\( 0.2 \)[/tex] kg.
These are the converted values for the given measurements.
