0.166 Repeating as a Fraction
The decimal number 0.166 repeating can be converted into a fraction. But before we dive into the conversion process, let's first understand what a repeating decimal is.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. In the case of 0.166 repeating, the sequence "6" repeats indefinitely, making it a repeating decimal.
Converting 0.166 Repeating into a Fraction
To convert 0.166 repeating into a fraction, we can use the following steps:
Step 1: Let x = 0.166...
Let's assume that x = 0.166...
Step 2: Multiply both sides by 1000
Multiply both sides of the equation by 1000, which gives us:
1000x = 166.166...
Step 3: Subtract the original equation from the new equation
Subtract the original equation x = 0.166... from the new equation 1000x = 166.166...:
1000x - x = 166.166... - 0.166...
Step 4: Simplify the equation
Simplify the equation by combining like terms:
999x = 166
Step 5: Divide both sides by 999
Divide both sides of the equation by 999, which gives us:
x = 166/999
Simplify the fraction
The fraction 166/999 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 37.
x = 166/999 = 1/6
Therefore, 0.166 repeating as a fraction is equal to 1/6.
Conclusion
In conclusion, the decimal number 0.166 repeating can be converted into a fraction, which is 1/6. This conversion process involves multiplying both sides of the equation by a power of 10, subtracting the original equation, and simplifying the resulting fraction.
