0.156 Recurring as a Fraction
In mathematics, a recurring decimal is a decimal that has a sequence of digits that repeats indefinitely. One such example is 0.156 recurring. But have you ever wondered what this recurring decimal represents as a fraction?
What is 0.156 Recurring?
The decimal 0.156 recurring can be written as 0.156156156... where the sequence "156" repeats indefinitely. This type of decimal is also known as a repeating decimal or a non-terminating decimal.
Converting 0.156 Recurring to a Fraction
To convert 0.156 recurring to a fraction, we can use the following steps:
- Let x = 0.156156... (where x is the recurring decimal)
- Multiply both sides of the equation by 1000 to get 1000x = 156.156156...
- Subtract the original equation from the new equation to get 999x = 156
- Divide both sides of the equation by 999 to get x = 156/999
Simplifying the Fraction
The fraction 156/999 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 156 and 999 is 33.
Divide both the numerator and the denominator by 33 to get:
156 ÷ 33 = 4 999 ÷ 33 = 27
So, the simplified fraction is 4/27.
Conclusion
In conclusion, the recurring decimal 0.156 recurring is equal to the fraction 4/27. This conversion is useful in various mathematical calculations and can help simplify complex problems.
