1/3 is equivalent to what
Understand the Problem
The question is asking to find an equivalent fraction or decimal representation of the fraction 1/3. We'll determine a common equivalent value for it.
Answer
The equivalent decimal representation of the fraction $\frac{1}{3}$ is $0.\overline{3}$.
Answer for screen readers
The equivalent decimal representation of the fraction $\frac{1}{3}$ is $0.333\ldots$ or $0.\overline{3}$.
Steps to Solve
- Finding the Decimal Representation
To convert the fraction $\frac{1}{3}$ into a decimal, you divide the numerator by the denominator.
$$ 1 \div 3 = 0.333\ldots $$
This decimal is repeating, meaning the 3 goes on indefinitely.
- Identifying the Equivalent Fraction
For equivalent fractions, you can multiply the numerator and the denominator by the same non-zero number.
For example, multiplying by 2:
$$ \frac{1 \times 2}{3 \times 2} = \frac{2}{6} $$
You can keep multiplying by any number to find more equivalents.
- Representing the Repeating Decimal
To express the repeating decimal clearly, you can use a bar notation:
$$ 0.333\ldots = 0.\overline{3} $$
This indicates that 3 repeats infinitely.
The equivalent decimal representation of the fraction $\frac{1}{3}$ is $0.333\ldots$ or $0.\overline{3}$.
More Information
The fraction $\frac{1}{3}$ demonstrates how fractions can have decimal forms that either terminate or repeat. The decimal representation of $\frac{1}{3}$ is particularly interesting because it shows the concept of repeating decimals, which is a common feature of many fractions.
Tips
- Confusing the decimal representation as terminating; remember that it is a repeating decimal, denoted as $0.\overline{3}$.
- Not simplifying the fraction correctly to find equivalent fractions; always multiply both the numerator and denominator by the same number.
