Consider the following statements :
`1/22` cannot be written as a terminating decimal
`2/15` can be written as a terminating decimal .
`1/16` can be written as a terminating decimal .
Which of the statement given below above is/are corect ?

Options

A. 1 only
B. 2 only
C. 1 and 3
D. 2 and 3

Answer

To determine which of the statements regarding the fractions is correct, we will analyze each statement one by one.

### Step 1: Analyze Statement 1 - `1/22`
1. Calculate the decimal value of `1/22`.
- When you divide 1 by 22, you get approximately `0.045454545...`, which is a repeating decimal (the digits "45" repeat indefinitely).
2. Since it does not terminate, **Statement 1 is correct**: `1/22` cannot be written as a terminating decimal.

### Step 2: Analyze Statement 2 - `2/15`
1. Calculate the decimal value of `2/15`.
- When you divide 2 by 15, you get approximately `0.133333...`, which is also a repeating decimal (the digit "3" repeats indefinitely).
2. Since it does not terminate, **Statement 2 is incorrect**: `2/15` cannot be written as a terminating decimal.

### Step 3: Analyze Statement 3 - `1/16`
1. Calculate the decimal value of `1/16`.
- When you divide 1 by 16, you get `0.0625`, which terminates after four decimal places.
2. Since it does terminate, **Statement 3 is correct**: `1/16` can be written as a terminating decimal.

### Conclusion
- The correct statements are:
- Statement 1: Correct
- Statement 2: Incorrect
- Statement 3: Correct

Thus, the correct statements are **1 and 3**.