<Question>
Write $\frac{3}{20}$ as a decimal.
</Question>

<think>
<Plan_1>
Okay, so I need to convert the fraction 3/20 into a decimal. Hmm, let's see. I remember that fractions can be turned into decimals by dividing the numerator by the denominator. So in this case, I should divide 3 by 20. But wait, 3 divided by 20... let me think about how division works here.

First, I know that 20 goes into 3 zero times because 20 is bigger than 3. So I'll need to add a decimal point and some zeros to continue the division. Let me write that out step by step.

None

<prompt_1.1> Set up the division of 3 by 20 and add a decimal point and zeros as needed. </prompt_1.1>
</Plan_1>

<Execution_1>
<execution_1.1>
So, 3 divided by 20. Set up the division as 3 ÷ 20. Since 20 can't go into 3, I write 0. and then proceed with the division. 

Next, I add a decimal point and a zero, making it 30. Now, how many times does 20 go into 30? That's once because 20 times 1 is 20. Subtract 20 from 30, and I get 10. Then, bring down another zero, making it 100. 

How many times does 20 go into 100? That's five times because 20 times 5 is 100. Subtract 100 from 100, and there's no remainder. So the division stops here. 

Putting it all together, 3 divided by 20 is 0.15.
</execution_1.1>
</Execution_1>

<Plan_2>
Based on execution_1.1:
Let me check if that's right. To verify, I can multiply 0.15 by 20 to see if I get back to 3.

<prompt_2.1> Verify the result by multiplying 0.15 by 20. </prompt_2.1>

Alternatively, maybe there's another way to convert 3/20 into a decimal without long division. Let me think. Sometimes, fractions can be converted by adjusting the denominator to make it a power of 10, since decimals are base 10. 

20 is the denominator here. What power of 10 can I get 20 to? Well, 10, 100, 1000... 20 times 5 is 100. So if I multiply both the numerator and denominator by 5, the denominator becomes 100, which is a power of 10.

<prompt_2.2> Use the method of converting the denominator to a power of 10 to verify the result. </prompt_2.2>
-----

Wait, but let me make sure I didn't make any mistakes in the multiplication. Let's recheck that step.

<prompt_2.3> Recheck the multiplication step in the alternative method. </prompt_2.3>

Another way to think about it: 20 is 1/5 of 100. So, multiplying numerator and denominator by 5 scales the fraction up by 5, turning 3/20 into (3*5)/(20*5) = 15/100.
</Plan_2>

<Execution_2>
<execution_2.1>
0.15 times 20: 0.15 multiplied by 10 is 1.5, so multiplied by 20 is double that, which is 3.
</execution_2.1>

<execution_2.2>
Let's try that. 

So, 3/20 multiplied by 5/5 is (3*5)/(20*5) = 15/100. 

15 divided by 100 is 0.15. That's the same result as before. So both methods give me 0.15.
</execution_2.2>

<execution_2.3>
3 times 5 is 15, and 20 times 5 is 100. So 15/100. Since the denominator is 100, that's two decimal places. The 1 is in the tenths place, and the 5 is in the hundredths place. So 15/100 is 0.15.
</execution_2.3>
</Execution_2>

<Plan_3>
Based on execution_2.2:
Therefore, both long division and adjusting the denominator give the same answer.
-----

Another check: 3/20. Let's break it down into smaller fractions. 3/20 is the same as 3 divided by 20. 

<prompt_3.1> Break down the fraction 3/20 into smaller fractions to verify the result. </prompt_3.1>
</Plan_3>

<Execution_3>
<execution_3.1>
Maybe think of it as (3/10)/2. Because 3/20 is equal to (3/10)/2. 

3 divided by 10 is 0.3. Then divide that by 2: 0.3 ÷ 2 = 0.15. Again, the same result. So multiple methods confirm that 3/20 is 0.15.
</execution_3.1>
</Execution_3>

<Final_answer>
Therefore, $\frac{3}{20}$ written as a decimal is $\boxed{0.15}$.
</Final_answer>
</think>