.42 Repeating as a Fraction
What is .42 Repeating?
.42 repeating is a decimal number that has a repeating pattern of 42 after the decimal point. It can be written as 0.424242... where the sequence of 42 continues indefinitely.
Converting .42 Repeating to a Fraction
To convert .42 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.424242...
Let's assume that the repeating decimal .42 can be represented by the variable x.
Step 2: Multiply both sides by 100
Multiplying both sides of the equation by 100, we get:
100x = 42.424242...
Step 3: Subtract the original equation from the new equation
Subtracting the original equation from the new equation, we get:
99x = 42
Step 4: Divide both sides by 99
Dividing both sides of the equation by 99, we get:
x = 42/99
Simplifying the Fraction
The fraction 42/99 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3.
x = 14/33
Therefore, the repeating decimal .42 can be represented as the fraction 14/33.
Conclusion
In conclusion, the repeating decimal .42 can be converted to a fraction by following the steps outlined above. The resulting fraction is 14/33, which is a simplified form of the original decimal.
