https://file.aiquickdraw.com/mathbot/file/1726406357774q8epde0l.jpg

The question in the image asks which student got the largest and smallest number when given cards with numbers in different bases. The bases for each student are as follows:

- **Rozita**: 241 in base 5.
- **Aishah**: 111100₂ (binary or base 2).
- **Helmy**: 110₂ (binary or base 2).
- **Osman**: 68₁₀ (decimal or base 10).
- **Maznah**: 114₈ (octal or base 8).

To solve this, we need to convert all these numbers to base 10 (decimal):

1. **Rozita**: 241₅ = \( 2 \times 5^2 + 4 \times 5^1 + 1 \times 5^0 = 2 \times 25 + 4 \times 5 + 1 \times 1 = 50 + 20 + 1 = 71₁₀ \)
2. **Aishah**: 111100₂ = \( 1 \times 2^5 + 1 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 0 \times 2^0 = 32 + 16 + 8 + 4 = 60₁₀ \)
3. **Helmy**: 110₂ = \( 1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 = 4 + 2 = 6₁₀ \)
4. **Osman**: 68₁₀ is already in base 10.
5. **Maznah**: 114₈ = \( 1 \times 8^2 + 1 \times 8^1 + 4 \times 8^0 = 1 \times 64 + 1 \times 8 + 4 = 64 + 8 + 4 = 76₁₀ \)

### Comparing the values:
- Rozita: 71
- Aishah: 60
- Helmy: 6
- Osman: 68
- Maznah: 76

The largest value is **Maznah (76)** and the smallest value is **Helmy (6)**.

Thus, the answer is:
- Largest value: **Maznah**.
- Smallest value: **Helmy**.

Would you like more details on the base conversions or have any other questions?

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Here are 5 related questions for further practice:

1. Convert 132₄ to base 10.
2. What is the base 10 equivalent of 10011₂?
3. How do you convert decimal numbers to base 8 (octal)?
4. Which is larger: 101010₂ or 52₁₀?
5. How do you determine the base from a given number?

**Tip:** Always ensure you break down powers systematically when converting between number bases to avoid mistakes.

Diagram 2 shows five students who were given number cards with different bases in a Mathematics quiz competition. Who got the largest value and the smallest value?

Learn how to convert numbers from various bases (base 2, base 5, base 8) to base 10 to determine the largest and smallest values. This example covers five students participating in a Mathematics quiz competition and helps you understand how to compare numbers in different base systems. Suitable for Grades 6-8.

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