Let's convert all the given numbers to the same base (base 10) for comparison.

1. $(1.1)_{\text{base } 2}$:

• The integer part "1" in base 2 is $1 \times 2^0 = 1$.
• The decimal part ".1" in base 2 is $1 \times 2^{-1} = 0.5$.
• So, $(1.1)_{\text{base } 2} = 1 + 0.5 = 1.5$ in base 10.

2. $(1.4)_{\text{base } 10}$ is already in base 10, so it stays $1.4$.

3. $(1.5)_{\text{base } 16}$:

• The integer part "1" in base 16 is $1 \times 16^0 = 1$.
• The decimal part ".5" in base 16 is $5 \times 16^{-1} = 5 \times \frac{1}{16} = 0.3125$.
• So, $(1.5)_{\text{base } 16} = 1 + 0.3125 = 1.3125$ in base 10.

Now, the numbers in base 10 are:

• $1.5$ (from $(1.1)_{\text{base } 2}$)
• $1.4$ (from $(1.4)_{\text{base } 10}$)
• $1.3125$ (from $(1.5)_{\text{base } 16}$)

Ordering them from smallest to largest: $(1.5)_{\text{base } 16} = 1.3125 < (1.4)_{\text{base } 10} = 1.4 < (1.1)_{\text{base } 2} = 1.5$

Thus, the order from smallest to largest is: $(1.5)_{\text{base } 16}, (1.4)_{\text{base } 10}, (1.1)_{\text{base } 2}$

Would you like further details or have any questions?

5 Related Questions:

1. How do you convert fractional numbers between different bases?
2. What are the general steps for converting from base 2 to base 10?
3. How does the base-16 system (hexadecimal) work in comparison to base 10?
4. How would the ordering change if we used different base numbers?
5. Can you explain how to add numbers from different bases?

Tip:

When converting fractional numbers between bases, treat each digit after the decimal point as a power of the base's reciprocal (e.g., in base 2, .1 is $1 \times 2^{-1}$).