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
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Set up division
To convert 1/3 to a decimal, we need to divide 1 by 3:
$1 \div 3$
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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.
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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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