Read the statements carefully and state T for true and F for false.
I. The place value of a digit at tenths place is 0.1 times the place value of same digit at the hundredths place.
II. ` ( 0.03)/( 0.3) + ( 3.3)/( 0.03) = 110.1`
III. Five and seven hundredths is written as 5.07

Options

A. `{:(I,II,III),(F,T,T):}`
B. `{:(I,II,III),(F,F,F):}`
C. `{:(I,II,III),(T,F,F):}`
D. `{:(I,II,III),(F,T,F):}`

Answer

To solve the question, we need to evaluate each of the three statements and determine whether they are true (T) or false (F).

### Statement I:
**The place value of a digit at tenths place is 0.1 times the place value of the same digit at the hundredths place.**

1. **Understanding Place Values:**
- The place value of a digit in the tenths place is calculated as \(0.1 \times a\) (where \(a\) is the digit).
- The place value of the same digit in the hundredths place is calculated as \(0.01 \times a\).

2. **Comparing the Values:**
- The statement claims that the tenths place value is \(0.1\) times the hundredths place value.
- Mathematically, this means:
\[ 0.1 \times (0.01 \times a) = 0.001 \times a \]
- This is incorrect because \(0.1\) times the hundredths place value should actually be:
\[ 0.1 \times (0.01 \times a) = 0.001 \times a \neq 0.1 \times a \]

3. **Conclusion:**
- Therefore, this statement is **False (F)**.

### Statement II:
**\((0.03)/(0.3) + (3.3)/(0.03) = 110.1\)**

1. **Calculating Each Fraction:**
- First, calculate \((0.03)/(0.3)\):
\[ \frac{0.03}{0.3} = \frac{3}{30} = 0.1 \]
- Next, calculate \((3.3)/(0.03)\):
\[ \frac{3.3}{0.03} = \frac{33}{0.3} = 110 \]

2. **Adding the Results:**
- Now, add the two results:
\[ 0.1 + 110 = 110.1 \]

3. **Conclusion:**
- Therefore, this statement is **True (T)**.

### Statement III:
**Five and seven hundredths is written as 5.07.**

1. **Understanding the Statement:**
- "Five and seven hundredths" means:
- 5 is the whole number.
- 7 hundredths means \(0.07\).

2. **Combining the Values:**
- Thus, the decimal representation will be:
\[ 5 + 0.07 = 5.07 \]

3. **Conclusion:**
- Therefore, this statement is **True (T)**.

### Final Answers:
- Statement I: F
- Statement II: T
- Statement III: T