What is the decimal form of 1/3?
Understand the Problem
The question is asking for the decimal representation of the fraction one-third. This will involve performing the division of 1 by 3.
Answer
The decimal representation of \( \frac{1}{3} \) is \( 0.333... \).
Answer for screen readers
The decimal representation of ( \frac{1}{3} ) is ( 0.333... ).
Steps to Solve
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Set up the division To find the decimal representation of ( \frac{1}{3} ), we need to divide 1 by 3.
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Perform long division When we set up 1.000 (adding decimal places), we start dividing:
- 3 goes into 1 zero times.
- We then consider 10 (adding a decimal) and find 3 goes into 10 three times (since ( 3 \times 3 = 9 )).
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Subtract and bring down the next digit After subtracting 9 from 10, we have: $$ 10 - 9 = 1 $$ Now, we bring down the next zero to get 10 again.
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Repeat the division process We repeat the previous step:
- 3 goes into 10 three times again.
- We subtract (9) from (10) to get (1), and then bring down another zero.
- Recognize the repeating pattern This process shows that we will keep getting 3 in the decimal places. The result can be written as: $$ 0.333... $$ This means that the decimal 3 repeats indefinitely.
The decimal representation of ( \frac{1}{3} ) is ( 0.333... ).
More Information
The decimal ( 0.333... ) is a repeating decimal. In mathematics, this notation signifies that the 3 continues infinitely. It can also be expressed as ( \frac{1}{3} ).
Tips
- Confusing terminating and repeating decimals: Some might think ( 0.3 ) is the final answer instead of recognizing it as repeating.
- Forgetting to include enough decimal places or writing an endpoint: It’s important to denote that the "3" continues indefinitely by using a bar over 3 or an ellipsis.
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