# 1/3 as a decimal

Converting 1/3 to a decimal involves division. Here’s how you can do it step by step:

Step 1: Understand the Fraction

1/3 means 1 divided by 3.

Step 2: Set Up the Division

Set up the division with 1 as the dividend and 3 as the divisor.

Step 3: Divide

1 is less than 3, so you can’t divide it as is. You add a decimal point to the 1 and bring down a zero, making it 10.
3 goes into 10 three times (9), and you subtract the product (10 – 9 = 1).

Step 4: Repeat

Because you have a remainder, bring down another zero and divide again. 3 goes into 10 three times, and you subtract the product (10 – 9 = 1).

This process repeats indefinitely because each time you will have a remainder of 1.

Step 5: Recognize the Pattern

Since the remainder repeats, the division will result in the digit 3 repeating endlessly.

Step 6: Write the Decimal

The decimal representation of 1/3 is 0.333…, which can be written with a bar notation as 0.\overline{3} to indicate that the 3 is repeating.