What is the decimal form of 1/3?

Understand the Problem

The question is asking for the decimal representation of the fraction one-third. The solution involves dividing 1 by 3 to convert it into decimal form.

Answer

0.3333...
Answer for screen readers

The decimal form of 1/3 is 0.3333... (repeating)

Steps to Solve

  1. Set up division

    To convert 1/3 to a decimal, we need to divide 1 by 3:

$1 \div 3$

  1. Perform long division

    Perform long division of 1 by 3:

$$\begin{array}{r} 0.3333...\ 3\enclose{longdiv}{1.0000...}\ \underline{0.9}\ 0.1000\ \underline{0.0999}\ 0.0001\ \end{array}$$

We see that the remainder of 1 keeps repeating, giving us a repeating decimal.

  1. Express final answer

    The result of the division is 0.3333..., where the 3 repeats infinitely. We can write this as:

$0.\overline{3}$ or $0.3\overline{3}$ or $0.3333...$

The decimal form of 1/3 is 0.3333... (repeating)

More Information

1/3 is a classic example of a repeating decimal. In fact, all fractions will result in either a terminating decimal or a repeating decimal when converted to decimal form.

Tips

A common mistake is to write the answer as 0.33 or 0.333, which are approximations. It's important to indicate that the 3 repeats infinitely, either by using an overline, ellipsis (...), or stating that it repeats.

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