Read the following statements carefully and state 'T' for true and 'F' for false.
(i) `(501)/(25)` is a terminating decimal.
(ii) `(621)/(125)` is a non-terminating decimal.
(iii) `(6805)/(27 xx 5^(2))` is a non-terminating decimal.
(iv) `(7105)/(7 xx 5^(2))` is a terminating decimal.

Options

A. `{:(i,ii,iii,iv),(F ,T,T,F):}`
B. `{:(i,ii,iii,iv),(T ,F,T,T):}`
C. `{:(i,ii,iii,iv),(T ,T,F,F):}`
D. `{:(i,ii,iii,iv),(F ,T,F,T):}`

Answer

To determine whether each statement is true or false regarding the nature of the decimals produced by the given fractions, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Statement (i):** \(\frac{501}{25}\) is a terminating decimal.
- To check if this is a terminating decimal, we can perform the division:
\[ \frac{501}{25} = 20.04 \]
- Since the result is a finite decimal, this statement is **True (T)**.

2. **Statement (ii):** \(\frac{621}{125}\) is a non-terminating decimal.
- Let's divide:
\[ \frac{621}{125} = 4.968 \]
- The result is also a finite decimal, which means it is terminating. Therefore, this statement is **False (F)**.

3. **Statement (iii):** \(\frac{6805}{27 \times 5^2}\) is a non-terminating decimal.
- First, calculate \(27 \times 5^2 = 27 \times 25 = 675\).
- Now, perform the division:
\[ \frac{6805}{675} \approx 10.08148 \]
- Since this result is a finite decimal, it is terminating. Thus, this statement is **False (F)**.

4. **Statement (iv):** \(\frac{7105}{7 \times 5^2}\) is a terminating decimal.
- First, calculate \(7 \times 5^2 = 7 \times 25 = 175\).
- Now, perform the division:
\[ \frac{7105}{175} = 40.06 \]
- This result is also a finite decimal, indicating it is terminating. Therefore, this statement is **True (T)**.

### Final Answers:
- (i) T
- (ii) F
- (iii) F
- (iv) T