0.142 Repeating as a Fraction
What is 0.142 Repeating?
0.142 repeating is a decimal number that has a repeating pattern of digits. The pattern in this case is "142" which repeats indefinitely. This type of decimal is known as a repeating decimal or a non-terminating decimal.
Converting 0.142 Repeating to a Fraction
To convert 0.142 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.142 repeating
Let's assign the value of 0.142 repeating to a variable x.
Step 2: Multiply x by 1000
Multiply both sides of the equation by 1000 to get rid of the decimal points.
1000x = 142.142...
Step 3: Subtract x from both sides
Subtract x from both sides of the equation to get:
999x = 142
Step 4: Solve for x
Divide both sides of the equation by 999 to solve for x.
x = 142/999
Step 5: Simplify the fraction
The fraction 142/999 can be simplified by dividing 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.
Therefore, 0.142 repeating as a fraction is 142/999.
Conclusion
In this article, we have learned how to convert the repeating decimal 0.142 repeating to a fraction. By following the steps outlined above, we can convert any repeating decimal to a fraction. The resulting fraction can be simplified by dividing both the numerator and the denominator by their GCD.
