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2/3 as a decimal




What is 2/3 as decimal? Let’s explore the exact steps how to convert a fraction to a decimal based on the below example

  1. Understand the Fraction: The fraction 23 means dividing 2 by 3.
  2. Set Up the Division: Position 2 as the dividend and 3 as the divisor.
  3. Perform the Division:
    • Since 2 is smaller than 3, you can’t divide it directly. Add a decimal point to 2 and append a zero, turning it into 20 (in the tenths place).
    • Divide 20 by 3. The result is 6 because 3 times 6 is 18, which is the closest you can get to 20 without going over.
    • Write 6 to the right of the decimal point in your answer.
  4. Subtract to Find the Remainder: Subtract 18 (3 times 6) from 20. The remainder is 2.
  5. Repeat the Process for the Remainder:
    • Add another zero to the remainder to make it 20 again (now working in the hundredths place).
    • Divide 20 by 3, which gives you 6 because 3 times 6 is 18.
    • Add this 6 to your answer, making it 0.66 so far.
  6. Check for Further Remainders: Subtract 18 from 20. The remainder is again 2, just like before.
  7. Recognize the Repeating Pattern:
    • This process will continue indefinitely, with each division of 20 by 3 resulting in 6, and leaving a remainder of 2.
    • This means that the decimal will have a repeating pattern of 6.
  8. Finalize the Answer: The decimal representation of 23 is 0.666…, where the digit 6 repeats endlessly.

In summary, 23 converts to the decimal 0.666…, a repeating decimal where the digit 6 continues infinitely. This is typical for fractions where the denominator does not factor into a product of only 2s and/or 5s, leading to such repeating decimals.

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

General rules: convert fraction to decimal

Practical examples:

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