0.1, 0.9, 0.01, 0.09 ______ 0.009

Options

A. `0.0001`
B. `0.1010 `
C. `0.01`
D. `0.001`

Answer

To solve the series: 0.1, 0.9, 0.01, 0.09, ____, 0.009, we need to identify the pattern in the sequence.

### Step-by-Step Solution:

1. **Identify the Terms**:
The given series is: 0.1, 0.9, 0.01, 0.09, ____, 0.009.

2. **Convert to Fractional Form**:
To better understand the relationship between the numbers, we can convert them into a more manageable form:
- 0.1 = 1/10
- 0.9 = 9/10
- 0.01 = 1/100
- 0.09 = 9/100
- 0.009 = 9/1000

3. **Look for a Pattern**:
Now, let's observe the pattern:
- The first two terms (0.1 and 0.9) can be seen as 1/10 and 9/10.
- The next two terms (0.01 and 0.09) are 1/100 and 9/100.
- The last term (0.009) is 9/1000.

4. **Identify the Missing Term**:
The missing term should logically fit between 0.09 (9/100) and 0.009 (9/1000).
If we follow the pattern of multiplying by 1/10, we can see:
- 0.1 (1/10) → 0.1 * (1/10) = 0.01 (1/100)
- 0.9 (9/10) → 0.9 * (1/10) = 0.09 (9/100)
- 0.01 (1/100) → 0.01 * (1/10) = 0.001 (1/1000)
- 0.09 (9/100) → 0.09 * (1/10) = 0.009 (9/1000)

5. **Conclusion**:
Therefore, the missing term in the series is 0.001.

### Final Answer:
The missing term is **0.001**.

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