The following are the steps inolved in converting `0.bar(23)` into p/q form where `q!=0`. Arrange them in sequential order from the first to the last.
A. `:.100x=23.23 23 23` ……….2
B.As periodicity is 2, multiply the Eq. 2 with 100.
C.`:.99x=23impliesx=23/99`
D. Let `x=0.bar(23)=0.23 23 23`........1
E. Subtract Eq. 1 from Eq 2

Options

A. DBEAC
B. DBAEC
C. DBCAE
D. DABEC

Answer

To convert the repeating decimal \(0.\overline{23}\) into the form \( \frac{p}{q} \), we can follow these steps in the correct order:

### Step-by-Step Solution:

1. **Let \( x = 0.\overline{23} = 0.232323...\)** (This is Step D)
- We start by defining \( x \) as the repeating decimal.

2. **Multiply both sides by 100** (This is Step B)
- Since the decimal repeats every two digits, we multiply by \( 100 \) to shift the decimal point two places to the right:
\[ 100x = 23.232323... \]

3. **Subtract the first equation from the second equation** (This is Step E)
- Now we subtract the first equation from the second:
\[ 100x - x = 23.232323... - 0.232323... \]
This simplifies to:
\[ 99x = 23 \]

4. **Solve for \( x \)** (This is Step C)
- Now we can solve for \( x \):
\[ x = \frac{23}{99} \]

5. **Final Result**:
- We have successfully converted \( 0.\overline{23} \) into the fraction \( \frac{23}{99} \).

### Sequential Order of Steps:
- D: Let \( x = 0.\overline{23} = 0.232323...\)
- B: Multiply both sides by 100
- E: Subtract the first equation from the second equation
- C: Solve for \( x \)