0.393 Repeating as a Fraction
What is 0.393 Repeating?
0.393 repeating, also known as 0.393..., is a non-terminating decimal that goes on indefinitely in a repeating pattern. The digits 3 and 9 repeat indefinitely, making it a periodic decimal.
Converting 0.393 Repeating to a Fraction
To convert 0.393 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.393...
Let x be equal to 0.393... .
Step 2: Multiply x by 1000
Multiply both sides of the equation by 1000 to get:
1000x = 393.393...
Step 3: Subtract x from 1000x
Subtract x from both sides of the equation to get:
999x = 393
Step 4: Divide by 999
Divide both sides of the equation by 999 to get:
x = 393/999
Step 5: Simplify the Fraction
Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 111.
x = 3/9
x = 1/3
Therefore, the fraction equivalent to 0.393 repeating is 1/3.
Conclusion
In this article, we have successfully converted 0.393 repeating to a fraction. The fraction equivalent to 0.393 repeating is 1/3. This method can be applied to convert any repeating decimal to a fraction.
