2/3 as a decimal

Converting 2/3 to a decimal involves a simple division process. Here’s the step-by-step method:

Step 1: Understand the Fraction

2/3 means 2 divided by 3.

Step 2: Set Up the Division

You set up the division with 2 as the dividend (the number being divided) and 3 as the divisor (the number you are dividing by).

Step 3: Divide

Since 2 is less than 3, you cannot divide it as it is. You add a decimal point to the 2 and bring down a zero, making it 20.

3 goes into 20 six times (18), and you subtract the product from 20, leaving a remainder of 2 (20 – 18 = 2).

Step 4: Repeat the Process

You once again bring down a zero to the remainder, making it 20, and divide by 3.
This process continues with the digit 6 repeating.

Step 5: Recognize the Pattern

Since you are always left with a remainder of 2, the division will result in the digit 6 repeating indefinitely.

Step 6: Write the Decimal

The decimal representation of 2/3 is 0.666…, which can be written with a bar notation as 0.\overline{6} to indicate that the 6 is repeating.