3.1 Repeating as a Fraction
The decimal number 3.1 repeating, also known as 3.111... or 3.(1), is a recurring decimal that can be expressed as a fraction. In this article, we will explore how to convert this repeating decimal to a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. In the case of 3.1 repeating, the digit 1 repeats indefinitely after the decimal point.
Converting 3.1 Repeating to a Fraction
To convert 3.1 repeating to a fraction, we can use the following steps:
Step 1: Let x = 3.1 Repeating
Let x = 3.1 repeating, which can also be written as x = 3.111...
Step 2: Multiply x by 10
Multiply both sides of the equation by 10, which gives us:
10x = 31.1 repeating
Step 3: Subtract x from 10x
Subtract x from both sides of the equation, which gives us:
9x = 28
Step 4: Divide by 9
Divide both sides of the equation by 9, which gives us:
x = 28/9
Result
Therefore, 3.1 repeating can be expressed as a fraction, which is:
3.1 Repeating = 28/9
This fraction is the equivalent of the repeating decimal 3.1.
Conclusion
In conclusion, we have successfully converted the repeating decimal 3.1 to a fraction, which is 28/9. This demonstrates that repeating decimals can be expressed as fractions, and vice versa. This conversion can be useful in various mathematical applications, such as algebra and geometry.
