3.333 as a fraction
Understand the Problem
The question is asking how to express the decimal number 3.333 as a fraction. To do this, we can convert the repeating decimal into a fraction in a step-by-step manner.
Answer
\( \frac{10}{3} \)
Answer for screen readers
The final answer is ( \frac{10}{3} )
Steps to Solve
- Express the repeating decimal as a variable
We assign the repeating decimal to a variable, let's call it $x$:
$$ x = 3.333... $$
- Multiply the variable to shift the decimal
We multiply $x$ by 10 to shift the decimal one place to the right:
$$ 10x = 33.333... $$
- Subtract the original variable
Now, we subtract the original variable equation from this new equation:
$$ 10x - x = 33.333... - 3.333... $$
This simplifies to:
$$ 9x = 30 $$
- Solve for the variable
Divide both sides by 9:
$$ x = \frac{30}{9} = \frac{10}{3} $$
Therefore, the repeating decimal 3.333... as a fraction is ( \frac{10}{3} ).
The final answer is ( \frac{10}{3} )
More Information
The fraction ( \frac{10}{3} ) is in its simplest form. It is interesting to note that any repeating decimal can be converted into a fraction using this method.
Tips
A common mistake is forgetting to properly shift the decimal or failing to align the subtraction step correctly, which may lead to incorrect simplification.
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