0.123 Recurring as a Fraction in its Simplest Form
What is a Recurring Decimal?
A recurring decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, 0.123123123... is a recurring decimal because the sequence "123" repeats indefinitely.
Converting 0.123 Recurring to a Fraction
To convert 0.123 recurring to a fraction, we can use the following steps:
Step 1: Let x = 0.123123...
Let's assume that x = 0.123123... is the recurring decimal we want to convert to a fraction.
Step 2: Multiply x by 1000
Multiplying x by 1000, we get:
1000x = 123.123123...
Step 3: Subtract x from 1000x
Subtracting x from 1000x, we get:
999x = 123
Step 4: Divide by 999
Dividing both sides by 999, we get:
x = 123/999
Step 5: Simplify the Fraction
Simplifying the fraction, we get:
x = 41/333
Therefore, 0.123 recurring as a fraction in its simplest form is 41/333.
Conclusion
In this article, we learned how to convert 0.123 recurring to a fraction in its simplest form using simple algebraic steps. The final answer is 41/333, which is the simplest form of the fraction.
