0.142 Recurring as a Fraction in Simplest Form
In this article, we will explore how to convert the recurring decimal 0.142 into a fraction in its simplest form.
What is a Recurring Decimal?
A recurring decimal is a decimal number that has a sequence of digits that repeats indefinitely. In the case of 0.142, the sequence "142" repeats indefinitely, making it a recurring decimal.
Converting a Recurring Decimal to a Fraction
To convert a recurring decimal to a fraction, we can use the following steps:
- Let the recurring decimal be x. In this case, x = 0.142.
- Multiply both sides of the equation by 10^3, where 3 is the number of digits in the repeating sequence.
- Simplify the equation by subtracting the original equation from the new equation.
- Solve for x.
Converting 0.142 to a Fraction
Let's follow the steps above to convert 0.142 to a fraction:
Step 1: Let x = 0.142.
Step 2: Multiply both sides of the equation by 10^3:
1000x = 142.142
Step 3: Subtract the original equation from the new equation:
999x = 142
Step 4: Solve for x:
x = 142/999
Simplifying the Fraction
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 142 and 999 is 1, so the fraction is already in its simplest form:
x = 142/999
Therefore, the recurring decimal 0.142 can be expressed as a fraction in its simplest form as 142/999.
