Find decimal expansion of `(17)/(8), (3)/(15), (2)/(7), (50)/(3)`.

Answer

To find the decimal expansions of the fractions \( \frac{17}{8}, \frac{3}{15}, \frac{2}{7}, \) and \( \frac{50}{3} \), we will perform long division for each fraction.

### Step 1: Decimal Expansion of \( \frac{17}{8} \)

1. Divide 17 by 8.
- 8 goes into 17 two times (since \( 8 \times 2 = 16 \)).
- Remainder: \( 17 - 16 = 1 \).
2. Add a decimal point and a zero to the remainder (making it 10).
- 8 goes into 10 one time (since \( 8 \times 1 = 8 \)).
- Remainder: \( 10 - 8 = 2 \).
3. Bring down another zero (making it 20).
- 8 goes into 20 two times (since \( 8 \times 2 = 16 \)).
- Remainder: \( 20 - 16 = 4 \).
4. Bring down another zero (making it 40).
- 8 goes into 40 five times (since \( 8 \times 5 = 40 \)).
- Remainder: \( 40 - 40 = 0 \).

Thus, \( \frac{17}{8} = 2.125 \).

### Step 2: Decimal Expansion of \( \frac{3}{15} \)

1. Divide 3 by 15.
- 15 goes into 3 zero times.
- Add a decimal point and a zero (making it 30).
- 15 goes into 30 two times (since \( 15 \times 2 = 30 \)).
- Remainder: \( 30 - 30 = 0 \).

Thus, \( \frac{3}{15} = 0.2 \).

### Step 3: Decimal Expansion of \( \frac{2}{7} \)

1. Divide 2 by 7.
- 7 goes into 2 zero times.
- Add a decimal point and a zero (making it 20).
- 7 goes into 20 two times (since \( 7 \times 2 = 14 \)).
- Remainder: \( 20 - 14 = 6 \).
2. Bring down another zero (making it 60).
- 7 goes into 60 eight times (since \( 7 \times 8 = 56 \)).
- Remainder: \( 60 - 56 = 4 \).
3. Bring down another zero (making it 40).
- 7 goes into 40 five times (since \( 7 \times 5 = 35 \)).
- Remainder: \( 40 - 35 = 5 \).
4. Bring down another zero (making it 50).
- 7 goes into 50 seven times (since \( 7 \times 7 = 49 \)).
- Remainder: \( 50 - 49 = 1 \).
5. Bring down another zero (making it 10).
- 7 goes into 10 one time (since \( 7 \times 1 = 7 \)).
- Remainder: \( 10 - 7 = 3 \).
6. Bring down another zero (making it 30).
- 7 goes into 30 four times (since \( 7 \times 4 = 28 \)).
- Remainder: \( 30 - 28 = 2 \).

This process will repeat, leading to a repeating decimal. Thus, \( \frac{2}{7} = 0.285714 \) (repeating).

### Step 4: Decimal Expansion of \( \frac{50}{3} \)

1. Divide 50 by 3.
- 3 goes into 50 sixteen times (since \( 3 \times 16 = 48 \)).
- Remainder: \( 50 - 48 = 2 \).
2. Add a decimal point and a zero (making it 20).
- 3 goes into 20 six times (since \( 3 \times 6 = 18 \)).
- Remainder: \( 20 - 18 = 2 \).

This process will repeat, leading to a repeating decimal. Thus, \( \frac{50}{3} = 16.666... \) (repeating).

### Summary of Decimal Expansions:
- \( \frac{17}{8} = 2.125 \)
- \( \frac{3}{15} = 0.2 \)
- \( \frac{2}{7} = 0.285714 \) (repeating)
- \( \frac{50}{3} = 16.666... \) (repeating)