0.123 Recurring as a Fraction
Introduction
A recurring decimal, also known as a repeating decimal, is a decimal that has a sequence of digits that repeats indefinitely. One example of a recurring decimal is 0.123 recurring, where the sequence "123" repeats indefinitely. In this article, we will explore how to convert 0.123 recurring as a fraction.
What is a Recurring Decimal?
A recurring decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, 0.12345678901234567890... is a recurring decimal, where the sequence "1234567890" repeats indefinitely.
How to Convert 0.123 Recurring as a Fraction
To convert 0.123 recurring as a fraction, we can use the following steps:
Step 1: Let the recurring decimal be x
Let 0.123 recurring be x. This means that x = 0.123123123...
Step 2: Multiply x by 1000
Multiply x by 1000 to get 1000x = 123.123123...
Step 3: Subtract x from 1000x
Subtract x from 1000x to get 999x = 123
Step 4: Divide by 999
Divide both sides of the equation by 999 to get x = 123/999
Step 5: Simplify the fraction
Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 111. This gives us x = 41/333
Therefore, 0.123 recurring as a fraction is 41/333.
Conclusion
In this article, we have learned how to convert 0.123 recurring as a fraction. By following the steps outlined above, we can convert any recurring decimal into a fraction. This skill is useful in various mathematical applications, including algebra and geometry.
