How to Convert Fractions to Decimals by Long Division Method | MathOGuide

Converting fractions to decimals using the long division method involves dividing the numerator by the denominator. Here's a step-by-step guide:

Example: Convert \(\frac{7}{4}\) to a decimal.

1. **Set up the division**:
Write 7 ÷ 4 using long division. 7 is the dividend, and 4 is the divisor.

2. **Divide**:
- Ask how many times 4 fits into 7. It fits *1* time.
- Write 1 above the division bar (the quotient).
- Multiply 1 by 4 to get 4, and subtract 4 from 7, leaving a remainder of 3.

3. **Bring down a zero**:
Since 4 doesn't go into 3, add a decimal point and bring down a zero, making the new dividend 30.

4. **Divide again**:
- Ask how many times 4 fits into 30. It fits *7* times.
- Write 7 after the decimal point.
- Multiply 7 by 4 to get 28, and subtract 28 from 30, leaving a remainder of 2.

5. **Repeat the process**:
- Bring down another zero, making the new dividend 20.
- 4 fits into 20 exactly *5* times.
- Write 5 after 1.75, and you're done! There’s no remainder, so the decimal terminates.

Final result:
\(\frac{7}{4} = 1.75\)

If there's no remainder after the division, the decimal terminates. If the division repeats, you'll get a repeating decimal.
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