What is 1 divided by 3 in decimal form?

1 divided by 3 in decimal form is 0.333..., which is known as a non-terminating and recurring decimal.

Understanding 1/3 as a Decimal

To express the fraction 1/3 as a decimal, you perform the division of the numerator (1) by the denominator (3). When you divide 1 by 3, the result is an infinite sequence of threes after the decimal point.

The process is as follows:

1. Set up the division: 1 ÷ 3.
2. Since 3 does not go into 1, write 0 and a decimal point, then add a zero to 1, making it 10.
3. Divide 10 by 3, which gives 3 with a remainder of 1 (3 × 3 = 9; 10 - 9 = 1).
4. Add another zero to the remainder 1, making it 10 again.
5. Repeat step 3: 10 divided by 3 is again 3 with a remainder of 1.

This pattern of getting a remainder of 1 and continually dividing 10 by 3 will continue indefinitely, resulting in an endless sequence of the digit 3.

Characteristics of the Decimal Form

The decimal representation of 1/3 has distinct characteristics:

• Non-terminating: This means the decimal digits go on forever and do not end. You can keep adding more threes, and the division will never have a zero remainder.
• Recurring (or Repeating): This indicates that one or more digits after the decimal point repeat infinitely in a predictable pattern. In the case of 1/3, the digit '3' is the repeating digit. This is often denoted with a vinculum (a bar) over the repeating digit, such as 0.$\overline{3}$.

Here's a quick overview:

Practical Implications

Because 1/3 is a non-terminating decimal, it cannot be written precisely with a finite number of decimal places. In practical applications, it is often approximated:

• 0.33 (rounded to two decimal places)
• 0.333 (rounded to three decimal places)
• 0.3333 (rounded to four decimal places)

These are approximations, and while they get closer to the exact value with more digits, they are never perfectly equal to 1/3. The exact decimal form requires the ellipsis (...) to signify its infinite nature.