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1/3 as a decimal




What is 1/3 as decimal? Let’s explore the exact steps how to convert a fraction to a decimal based on the below example

  • Understand the Fraction: The fraction 13  represents the division of 1 by 3.
  • Set Up the Division: Write down the division with 1 as the dividend (the number to be divided) and 3 as the divisor (the number to divide by).
  • Perform the Division:
    • Since 1 is smaller than 3, direct division is not possible. Add a decimal point to the dividend (1) and append a zero, making it 10 (in the tenths place).
    • Divide 10 by 3. The result is 3, since 3 times 3 is 9, which is the closest you can get to 10 without exceeding it.
    • Write down 3 to the right of the decimal point in your answer.
  • Subtract to Find the Remainder: Subtract 9 (3 times 3) from 10. The remainder is 1.
  • Repeat the Process for the Remainder:
    • Add another zero to the remainder to make it 10 (now working in the hundredths place).
    • Again, divide 10 by 3, which gives you 3 because 3 times 3 is 9.
    • Add this 3 to your answer, making it 0.33 so far.
  • Check for Further Remainders: Subtract 9 from 10. The remainder is 1, the same as before.
  • Continue the Process:
    • You’ll find that each time you add a zero to the remainder and divide by 3, you’ll get 3, and a remainder of 1.
    • This means the pattern will continue indefinitely.
  • Recognize the Repeating Decimal: Since the remainder repeats continuously, 13  is a repeating decimal. The decimal representation is 0.333…, where the 3 repeats endlessly.

Explore variety of examples below (the above steps are followed):

General rules: convert fraction to decimal

Practical examples:

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