Alright, let's begin by addressing the given questions step-by-step:
### Part (i): Convert the shorter two edges of the garden into binary numbers.
#### 1. Converting 5 meters to a binary number:
- We need to convert the decimal number 5 to binary.
- The binary representation of 5 is `101`.
- Therefore, 5 meters in binary is `0b101`.
#### 2. Converting 12 meters to a binary number:
- We need to convert the decimal number 12 to binary.
- The binary representation of 12 is `1100`.
- Therefore, 12 meters in binary is `0b1100`.
### Summary of Part (i):
- The binary representation of 5 meters is `0b101`.
- The binary representation of 12 meters is `0b1100`.
### Part (ii): Convert the shorter two edges of the garden into quinary numbers.
#### 1. Converting 5 meters to a quinary number:
- A quinary number system uses base 5.
- We need to convert the decimal number 5 to a quinary representation.
- Dividing 5 by 5, we get quotient 1 and remainder 0:
- 5 / 5 = 1, remainder = 0
- Dividing 1 by 5, we get quotient 0 and remainder 1:
- 1 / 5 = 0, remainder = 1
- Therefore, read the remainders in reverse order, we get `10`.
- Hence, 5 meters in quinary is `10`.
#### 2. Converting 12 meters to a quinary number:
- We need to convert the decimal number 12 to a quinary representation.
- Dividing 12 by 5, we get quotient 2 and remainder 2:
- 12 / 5 = 2, remainder = 2
- Dividing 2 by 5, we get quotient 0 and remainder 2:
- 2 / 5 = 0, remainder = 2
- Therefore, read the remainders in reverse order, we get `22`.
- Hence, 12 meters in quinary is `22`.
### Summary of Part (ii):
- The quinary representation of 5 meters is `10`.
- The quinary representation of 12 meters is `22`.
### Final Summary:
1. The binary representations:
- 5 meters = `0b101`
- 12 meters = `0b1100`
2. The quinary representations:
- 5 meters = `10`
- 12 meters = `22`
Thus, we have successfully converted the edges of the garden to both binary and quinary numbers.
