To convert a fraction to a decimal using long division, divide the numerator (the top number) by the denominator (the bottom number).
Here's a step-by-step breakdown:
- Set up the long division problem: Write the denominator outside the division symbol and the numerator inside.
- Divide: Perform the long division as you normally would. If the denominator doesn't go into the numerator evenly, add a decimal point and a zero to the numerator inside the division symbol. Treat the numerator followed by the decimal point and zero as if it were a whole number.
- Continue Dividing: Bring down the zero and continue dividing. You may need to add more zeros after the decimal point in the numerator to continue the division until you get a remainder of zero or reach the desired level of accuracy (e.g., rounding to the nearest hundredth).
- Place the decimal point: The decimal point in the quotient (the answer) should be directly above the decimal point in the dividend (the numerator).
- The result is your decimal: The number you get as the quotient is the decimal equivalent of the fraction.
Example:
Convert 3/4 to a decimal using long division:
- Set up the problem: 4 | 3
- 4 doesn't go into 3, so add a decimal point and a zero: 4 | 3.0
- 4 goes into 30 seven times (4 x 7 = 28). Write 7 above the 0 after the decimal point in 3.0.
- Subtract 28 from 30, which leaves a remainder of 2.
- Add another zero to the numerator: 4 | 3.00
- Bring down the new zero, making it 20.
- 4 goes into 20 five times (4 x 5 = 20). Write 5 above the second 0 after the decimal point in 3.00.
- Subtract 20 from 20, which leaves a remainder of 0.
Therefore, 3/4 = 0.75
