0.152 Recurring as a Fraction
What is 0.152 Recurring?
0.152 recurring, also written as 0.152..., is a decimal number that has a repeating pattern of 152 indefinitely. This type of decimal is known as a recurring decimal or a repeating decimal.
Converting 0.152 Recurring to a Fraction
To convert 0.152 recurring to a fraction, we can use a simple method. Let's start by assuming that the recurring decimal is equal to a variable, x.
Let x = 0.152...
Multiply both sides of the equation by 100 to shift the decimal point two places to the right.
100x = 15.152...
Now, subtract the original equation from the new equation to eliminate the recurring decimal.
99x = 15
Divide both sides of the equation by 99 to solve for x.
x = 15/99
Simplifying the Fraction
The fraction 15/99 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD).
GCD of 15 and 99 = 3
Divide both the numerator and the denominator by 3.
x = 5/33
Therefore, 0.152 recurring as a fraction is 5/33.
Conclusion
In conclusion, we have successfully converted 0.152 recurring to a fraction, which is 5/33. This method can be applied to any recurring decimal to convert it to a fraction.
