Convert Fraction to Decimal Using Long Division
Convert a fraction to a decimal by dividing the numerator by the denominator, e.g. 21 ÷ 16 = 1.3125. It either ends as a terminating decimal or repeats forever as a recurring decimal.
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How Do We Convert Simple Fractions to Decimals?
- Some fractions can be changed into decimals by rewriting them over 10, 100, or 1000.
- Example:
Converting Fractions to Decimals Using Long Division
- Divide the numerator by the denominator.
- Stop dividing when the remainder becomes 0.
- For example,
What Are Terminating and Recurring Decimals?
- A terminating decimal ends after a fixed number of digits.
- A recurring decimal has digits that repeat forever.
How Do We Find Recurring Decimals Using Long Division?
- Stop dividing when you see the same remainder again.
- Example:
Practice Questions
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Convert to a decimal.
Correct! 🎉 +10 pointsNot quite right
To convert 11/20 to a decimal, divide 11 by 20. The result is 0.55.
What is as a decimal?
Correct! 🎉 +10 pointsNot quite right
To convert 13/50 to a decimal, divide 13 by 50. The result is 0.26.
What is as a decimal?
Correct! 🎉 +20 pointsNot quite right
To convert 7/8 to a decimal, divide 7 by 8. The result is 0.875.
Convert to a decimal.
Correct! 🎉 +20 pointsNot quite right
To convert 131/99 to a decimal, divide 131 by 99. The result is a repeating decimal, 1.323232....
What is the decimal equivalent of ?
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To convert 7/9 to a decimal, divide 7 by 9. The result is a repeating decimal, 0.777....
Convert to a decimal.
Correct! 🎉 +30 pointsNot quite right
To convert 87/16 to a decimal, divide 87 by 16. The exact result is 5.4375.
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A terminating decimal stops after a finite number of digits. This happens when long division ends with a remainder of zero. A recurring decimal repeats one or more digits indefinitely. This happens when long division never gives a remainder of zero and the same digit keeps reappearing in the quotient.
Write the decimal as normal up to the point where the repeating digit, or block of digits, begins. Then mark each repeating digit with a dot above it. For 41/12, the answer is written as 3.41 with a dot above the 6. This is because the 6 repeats indefinitely after the first two decimal places.
Stop when the remainder reaches zero, because the decimal terminates and the answer is complete. You can also stop when the same remainder keeps appearing and the same digit keeps being added to the quotient. At that point you have spotted a recurring decimal. Further steps will only repeat the same pattern.
No. If the denominator scales easily to 10 or 100, you can convert by simplifying. Examples include two-fifths and three-quarters. For trickier fractions like twenty-one sixteenths, the denominator does not scale neatly. Here long division is the reliable universal method to use.
Yes. Long division is the universal method that works for every fraction. The result is either a terminating decimal or a recurring decimal. A terminating decimal happens when the remainder reaches zero. A recurring decimal has one or more digits that repeat indefinitely after the decimal point.