Converting a fraction to a decimal involves performing a division where the numerator (the top part of the fraction) is divided by the denominator (the bottom part of the fraction). Here’s a step-by-step guide:
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Identify the numerator and denominator: For the fraction \( \frac{a}{b} \), \( a \) is the numerator and \( b \) is the denominator.
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Perform the division: Divide \( a \) by \( b \). This can be done using long division or a calculator.
- If using long division:
- Set up the long division with \( a \) (the numerator) under the division bar and \( b \) (the denominator) outside.
- Divide as you would with whole numbers. If the numerator is smaller than the denominator, you'll start with a decimal point and add zeros to the numerator as needed.
- Continue dividing until you reach a remainder of 0 or until you have enough decimal places.
- If using long division:
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Result: The result of the division is the decimal equivalent of the fraction.
Example:
Convert \( \frac{3}{4} \) to a decimal.
- Identify the numerator and denominator: Numerator = 3, Denominator = 4.
- Perform the division: \( 3 \div 4 = 0.75 \).
- Result: \( \frac{3}{4} = 0.75 \).
Additional Tips:
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If the division ends with a remainder that becomes a repeating decimal (like \( \frac{1}{3} = 0.333... \)), you can indicate this by placing a bar over the repeating digit or writing it in a rounded form, like \( 0.33 \) or \( 0.3\overline{3} \).
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You can verify your result by multiplying the decimal back by the denominator to see if you return to the numerator. For example, \( 0.75 \times 4 = 3 \).
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