Read the statement carefully and state 'T' for true and 'F' for false.
(P) A fraction is said to be in simplest form if its numerator and denominator have no common factor other 1 .
(Q) `(5)/(9)` is greater than `(4)/(5)` .
(R ) Fraction can't be represented on the number line .
(S) In the place value of decimals , as we go from left to right , the multiplying factor becomes `(1)/(10)` of the previous factor .

Options

A. `{:("(P)" ,, "(Q)" ,, "( R)" ,, "(S)") , ("T" ,, "F" ,, "F" ,, "T"):}`
B. `{:("(P)" ,, "(Q)" ,, "( R)" ,, "(S)") , ("T" ,, "T" ,, "F" ,, "T"):}`
C. `{:("(P)" ,, "(Q)" ,, "( R)" ,, "(S)") , ("F" ,, "T" ,, "F" ,, "F"):}`
D. `{:("(P)" ,, "(Q)" ,, "( R)" ,, "(S)") , ("F" ,, "T" ,, "T" ,, "F"):}`

Answer

To solve the question, we need to evaluate each statement (P, Q, R, S) and determine whether they are true (T) or false (F).

### Step-by-Step Solution:

1. **Statement P**: "A fraction is said to be in simplest form if its numerator and denominator have no common factor other than 1."
- To determine if this statement is true, we recall the definition of a fraction in simplest form. A fraction is in simplest form when the greatest common divisor (GCD) of the numerator and denominator is 1. This means they share no common factors other than 1.
- **Conclusion**: This statement is true (T).

2. **Statement Q**: "5/9 is greater than 4/5."
- To compare these two fractions, we can convert them to a common denominator or cross-multiply.
- The denominators are 9 and 5. The least common multiple (LCM) of 9 and 5 is 45.
- Convert both fractions:
- \( \frac{5}{9} = \frac{5 \times 5}{9 \times 5} = \frac{25}{45} \)
- \( \frac{4}{5} = \frac{4 \times 9}{5 \times 9} = \frac{36}{45} \)
- Now we compare \( \frac{25}{45} \) and \( \frac{36}{45} \). Since 25 is less than 36, \( \frac{5}{9} < \frac{4}{5} \).
- **Conclusion**: This statement is false (F).

3. **Statement R**: "Fractions can't be represented on the number line."
- We know that fractions can be represented on the number line. For example, if we take the fraction \( \frac{1}{2} \), it can be marked exactly halfway between 0 and 1 on the number line.
- **Conclusion**: This statement is false (F).

4. **Statement S**: "In the place value of decimals, as we go from left to right, the multiplying factor becomes \( \frac{1}{10} \) of the previous factor."
- In decimal numbers, each digit to the right of the decimal point represents a value that is \( \frac{1}{10} \) of the value to its left. For example, in the decimal 65.4321:
- 6 is in the tens place (10^1),
- 5 is in the ones place (10^0),
- 4 is in the tenths place (10^-1),
- 3 is in the hundredths place (10^-2), and so on.
- This confirms that the multiplying factor decreases by a factor of \( \frac{1}{10} \) as we move left to right.
- **Conclusion**: This statement is true (T).

### Final Answers:
- P: T
- Q: F
- R: F
- S: T

### Summary:
The answers are:
- P: T
- Q: F
- R: F
- S: T