To convert a remainder in long division to a decimal, you essentially continue the division process beyond the whole number. Here's a breakdown of the steps:
-
Add a Decimal Point and Zero: After you've reached the end of the dividend (the number being divided) and have a remainder, add a decimal point to the dividend and write a zero after the decimal point. This does not change the value of the original dividend but allows you to continue the division.
-
Bring Down the Zero: Bring down the zero you just added next to the remainder, forming a new number to divide.
-
Continue Dividing: Divide the new number by the divisor (the number you're dividing by). Write the result (the quotient) after the decimal point in the quotient section (the answer).
-
Repeat if Necessary: If you still have a remainder, add another zero to the dividend (after the decimal point), bring it down, and continue dividing. Repeat this process until you get a remainder of zero (the division terminates) or you reach the desired level of decimal precision.
Example:
Let's say you're dividing 25 by 4 using long division.
- 4 goes into 25 six times (6 x 4 = 24).
- You subtract 24 from 25, leaving a remainder of 1.
- To convert the remainder to a decimal:
- Add a decimal point and a zero to 25, making it 25.0.
- Bring down the zero next to the remainder 1, making it 10.
- Divide 10 by 4. 4 goes into 10 two times (2 x 4 = 8). Write "2" after the decimal point in the quotient (6.2).
- Subtract 8 from 10, leaving a remainder of 2.
- Add another zero to 25.0, making it 25.00. Bring down the zero next to the remainder 2, making it 20.
- Divide 20 by 4. 4 goes into 20 five times (5 x 4 = 20). Write "5" after the "2" in the quotient (6.25).
- Subtract 20 from 20, leaving a remainder of 0. The division terminates.
Therefore, 25 divided by 4 is 6.25.
In essence, you are treating the remainder as the numerator of a fraction with the divisor as the denominator (1/4 in the first step of the example). By adding a decimal point and zeros, you are essentially finding the decimal equivalent of that fraction and adding it to the whole number quotient. You are effectively dividing the remainder by the divisor.
