These are four questions and four answers
Question 1. What does it mean to "convert" from one unit to another? Give an example.
Convert from one unit to another is transforming or changing the magnitude to an equivalent measure according to a different pattern of comparison or unit of measure.
For example, converting from meter to centimeters, means to transform the unit of measure (the pattern of comparison) from meter to centimeter.
When your measure is 3 meters, means the length is 3 times the standard pattern named meter.
Therefore, converting it to centimeters means that you want to know how many times is 3 meters relative to the a new pattern named centimeter.
Since, 1 meter equals 100 cm, you build a conversion factor which you can use to make the conversion:
1 m = 100 cm ⇒ 1 = 100 cm / 1 m
∴ 3 m = 3 m × 100 cm / 1 m = 300 cm.
Question 2. What are the general mathematical operations you use when converting from one SI unit to another?
The most common mathematical operations are the basic ones: addition, substraction, multiplication and division.
See one example of each one:
a) Addition:
Transform 20°C to K: 20 + 273.15 K = 293.15 K
b) Subtraction:
Convert 300 K to celsius degrees: 300 - 273.15°C = 26.85°C
c) Multiplication
Convert 1000 Km to meter
1000 Km × 1000 m/Km = 1,000,000 m
d) Division
Convert 1540 mm Hg to atm
1 atm = 760 mmHg ⇒ 1 = 760 mmHg / atm
1540 mmHg / (760 mmHg / atm) = 2.026 atm
Question 3. How many meters do you cover in a 10 km (10-K) race?
This requires to convert 10 km to the equivalent number of meters.
Conversion factor: 1 km = 1000 m ⇒ 1 = 1000 m/Km
∴ 10 Km = 10 Km × 1000 m/km = 10,000 m ← answer.
Quesiton 4. An Olympic swimming pool is 50 meters long. You swim from one end to the other four times.
a. How many meters do you swim?
4 laps × 50 m/lap = 200 m ← answer
b. How many kilometers do you swim?
1 = 1 km / 1000m
200 m = 200 × 1 km / 1000 m = 0.200 km ← answer
c. How many centimeters do you swim?
1 m = 100 cm ⇒ 1 = 100 cm / m
200 m = 200 m × 100 cm/m = 20,000 cm ← answer