If `a=(1/10)^(2), b=1/5` and `c =1/10`, then which of the following statements is CORRECT ?

Options

A. `a lt b lt c`
B. `a lt c lt b`
C. `b lt c lt a`
D. `c lt a lt b`

Answer

To solve the problem, we need to evaluate the values of \( a \), \( b \), and \( c \) given in the question and compare them to determine which statement is correct.

### Step 1: Calculate the value of \( a \)
Given:
\[ a = \left(\frac{1}{10}\right)^2 \]
Calculating \( a \):
\[ a = \frac{1}{10} \times \frac{1}{10} = \frac{1}{100} \]

### Step 2: Calculate the value of \( b \)
Given:
\[ b = \frac{1}{5} \]
Calculating \( b \):
\[ b = 0.2 \]

### Step 3: Calculate the value of \( c \)
Given:
\[ c = \frac{1}{10} \]
Calculating \( c \):
\[ c = 0.1 \]

### Step 4: Compare the values of \( a \), \( b \), and \( c \)
Now we have:
- \( a = \frac{1}{100} = 0.01 \)
- \( b = 0.2 \)
- \( c = 0.1 \)

### Step 5: Determine the correct statement
Now we can compare the values:
- \( a < c < b \)
- \( 0.01 < 0.1 < 0.2 \)

### Conclusion
The correct order of the values is:
\[ a < c < b \]
Thus, the correct statement is that \( a \) is less than \( c \), and \( c \) is less than \( b \).