To solve the problem and find the equivalent ratio to 5 cm : 5 m : 0.02 km, follow these steps:
1. Convert all measurements to the same unit:
- We need to convert 5 meters (m) and 0.02 kilometers (km) to centimeters (cm).
- Convert meters to centimeters:
[tex]\[ 1 \text{ meter} = 100 \text{ centimeters} \][/tex]
[tex]\[ 5 \text{ meters} = 5 \times 100 = 500 \text{ centimeters} \][/tex]
- Convert kilometers to centimeters:
[tex]\[ 1 \text{ kilometer} = 100,000 \text{ centimeters} \][/tex]
[tex]\[ 0.02 \text{ kilometers} = 0.02 \times 100,000 = 2000 \text{ centimeters} \][/tex]
2. Establish the ratio in centimeters:
- Now we have the ratio in centimers:
[tex]\[ 5 \text{ cm} : 500 \text{ cm} : 2000 \text{ cm} \][/tex]
3. Simplify the ratio:
- To simplify, divide each term by the smallest value, which is 5 cm.
- Divide each term by 5:
[tex]\[ 5 \div 5 = 1 \][/tex]
[tex]\[ 500 \div 5 = 100 \][/tex]
[tex]\[ 2000 \div 5 = 400 \][/tex]
- The simplified ratio is:
[tex]\[ 1 : 100 : 400 \][/tex]
Hence, the correct answer is:
B. 1 : 100 : 400
