0.142 42 Recurring as a Fraction
What is a Recurring Decimal?
A recurring decimal is a decimal number that has a sequence of digits that repeats indefinitely. In other words, it is a decimal that has a never-ending sequence of digits that follows a pattern. For example, the decimal 0.142 42 is a recurring decimal because the sequence "42" keeps repeating indefinitely.
Converting 0.142 42 to a Fraction
To convert the recurring decimal 0.142 42 to a fraction, we can use the following steps:
Step 1: Let x = 0.142 42
Let's let x equal the recurring decimal 0.142 42.
Step 2: Multiply both sides by 100
To get rid of the decimal point, we can multiply both sides of the equation by 100.
100x = 14.242 42
Step 3: Subtract the original equation from the new equation
Subtract x from both sides of the equation to get:
99x = 14.1
Step 4: Divide both sides by 99
Divide both sides of the equation by 99 to get:
x = 14.1 / 99
Step 5: Simplify the fraction
Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
x = 141 / 990
x = 71 / 495
Therefore, the recurring decimal 0.142 42 is equal to the fraction 71 / 495.
Conclusion
In this article, we have successfully converted the recurring decimal 0.142 42 to a fraction. The fraction equivalent to the recurring decimal is 71 / 495. This method can be applied to convert any recurring decimal to a fraction.
