.42 Repeating as a Fraction
Have you ever wondered how to convert a repeating decimal into a fraction? In this article, we'll explore how to convert .42 repeating as a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, .42 repeating is a repeating decimal because the sequence "42" repeats indefinitely: .42424242...
Converting .42 Repeating to a Fraction
To convert .42 repeating to a fraction, we can use the following steps:
Step 1: Let x = .42 repeating
Let x = .424242...
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get rid of the decimal point:
100x = 42.424242...
Step 3: Subtract x from 100x
Subtract x from both sides of the equation to eliminate the repeating decimal:
100x - x = 42.424242... - .424242...
This simplifies to:
99x = 42
Step 4: Divide by 99
Divide both sides of the equation by 99 to solve for x:
x = 42/99
Step 5: Simplify the Fraction
Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3:
x = 14/33
Therefore, .42 repeating as a fraction is equal to 14/33.
Conclusion
In this article, we've shown how to convert .42 repeating to a fraction using a simple 5-step process. By following these steps, you can convert any repeating decimal to a fraction.
