Example 7 Given that $$ a=0.1 $$ and $$ b=0.2 $$, put the following expressions in ascending order: - $$ a b=0.02 $$ - $$ \frac{a}{b} $$ - $$ b-a $$ - $$ \frac{a^{2}}{b^{2}} $$

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1. **Substitute the values of $$a$$ and $$b$$:**

Given $$a=0.1$$ and $$b=0.2$$, compute each expression.

2. **Compute $$ ab $$:**

$$
   ab = 0.1 \times 0.2 = 0.02
   $$

3. **Compute $$ \frac{a}{b} $$:**

$$
   \frac{a}{b} = \frac{0.1}{0.2} = 0.5
   $$

4. **Compute $$ b-a $$:**

$$
   b - a = 0.2 - 0.1 = 0.1
   $$

5. **Compute $$ \frac{a^{2}}{b^{2}} $$:**

$$
   \frac{a^{2}}{b^{2}} = \frac{(0.1)^2}{(0.2)^2} = \frac{0.01}{0.04} = 0.25
   $$

6. **Arrange the values in ascending order:**

$$
   ab = 0.02, \quad b-a = 0.1, \quad \frac{a^{2}}{b^{2}} = 0.25, \quad \frac{a}{b} = 0.5
   $$

7. **Final answer in ascending order:**

$$
   ab, \quad b-a, \quad \frac{a^{2}}{b^{2}}, \quad \frac{a}{b}
   $$
The expressions in ascending order are: 1. $$ ab = 0.02 $$ 2. $$ b - a = 0.1 $$ 3. $$ \frac{a^{2}}{b^{2}} = 0.25 $$ 4. $$ \frac{a}{b} = 0.5 $$

Example 7
Given that and , put the following expressions in ascending order:

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Example 7 Given that and , put the following expressions in ascending order: