Class Notes: Converting Fractions to Decimals Using Long Division

Objective

Learn how to convert fractions into decimals using the long division method.

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Steps to Convert a Fraction to a Decimal

1. Set up the Problem

   • Divide the numerator (top number) by the denominator (bottom number).
   • Write the numerator inside the division bracket (dividend) and the denominator outside (divisor).

2. Perform Long Division

   • If the numerator is smaller than the denominator, add a decimal point and zeroes to the right of the numerator.
   • Place a decimal point in the quotient as well.

3. Divide

   • Determine how many times the divisor fits into the current number.
   • Multiply the divisor by this result and subtract the product from the current number.
   • Bring down another zero if the remainder is not zero.
   • Repeat division steps until the remainder is zero (or desired decimal places are reached).

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Example 1: ( \frac{1}{5} )

• Set up as 1 divided by 5.
• 5 does not go into 1. Add a decimal point; now consider 10.
• 5 goes into 10 two times. ( 5 \times 2 = 10 ).
• Subtract ( 10-10=0 ).
• Quotient is 0.2

Conclusion:
( \frac{1}{5} = 0.2 )

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Example 2: ( \frac{1}{4} )

• Set up as 1 divided by 4.
• 4 does not go into 1. Add a decimal point and zero.
• 4 goes into 10 two times. ( 4 \times 2 = 8 ).
• Subtract ( 10-8=2 ).
• 4 does not go into 2. Bring down a zero (making 20).
• 4 goes into 20 five times. ( 4 \times 5 = 20 ).
• Subtract ( 20-20=0 ).
• Quotient is 0.25

Conclusion:
( \frac{1}{4} = 0.25 )

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Example 3: ( \frac{5}{8} )

• Set up as 5 divided by 8.
• 8 does not go into 5. Add a decimal point and zeros.
• 8 goes into 50 six times. ( 8 \times 6 = 48 ).
• Subtract ( 50-48=2 ).
• 8 does not go into 2. Bring down a zero (making 20).
• 8 goes into 20 two times. ( 8 \times 2 = 16 ).
• Subtract ( 20-16=4 ).
• Bring down another zero (making 40).
• 8 goes into 40 five times. ( 8 \times 5 = 40 ).
• Subtract ( 40-40=0 ).
• Quotient is 0.625

Conclusion:
( \frac{5}{8} = 0.625 )

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Key Points

• Always divide numerator by denominator.
• Add decimal points and zeros as needed to continue division.
• Continue dividing until there's no remainder or until you reach the desired number of decimal places.
• The final quotient is the decimal representation of the fraction.

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Practice

• To reinforce the process, try converting other fractions to decimals using these steps!