What is 1/9 in decimal form?
Understand the Problem
The question is asking for the decimal representation of the fraction 1/9. To solve this, we will divide 1 by 9 to find its decimal equivalent.
Answer
The decimal representation of the fraction $\frac{1}{9}$ is $0.\overline{1}$.
Answer for screen readers
The decimal representation of the fraction $\frac{1}{9}$ is $0.\overline{1}$.
Steps to Solve
- Set up the division problem
We need to divide 1 by 9. This can be expressed as the division problem: $$ 1 \div 9 $$
- Perform the division
When we divide, we can write 1 as 1.000000 to see the decimal. So, we perform the long division.
- 9 does not go into 1, so we have 0.
- We add a decimal point and a zero, making it 10.
- 9 goes into 10 one time with a remainder.
This gives us: $$ 0.1 $$
- Continue the division
Now, we bring down another zero making it 10 again.
- 9 still goes into 10 one time, again with a remainder.
- Repeat this process.
This will lead us to: $$ 0.1111... $$ (which is an infinite series of 1s)
- Identify the decimal representation
The decimal representation of the fraction $ \frac{1}{9} $ is $ 0.\overline{1} $ indicating that 1 repeats infinitely.
The decimal representation of the fraction $\frac{1}{9}$ is $0.\overline{1}$.
More Information
The decimal $0.\overline{1}$ means that the digit 1 continues infinitely. This is a common example of a repeating decimal, where a single digit or a group of digits repeats indefinitely.
Tips
- A common mistake is stopping the division too early and writing $0.1$ instead of recognizing the repeating decimal $0.\overline{1}$.
- It's important to realize when a pattern emerges in the decimal and to represent it properly.
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