0.123 Repeating as a Simplified Fraction
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. One example of a repeating decimal is 0.123 repeating, which can be written as 0.123123123... . But did you know that repeating decimals can be expressed as simplified fractions?
Converting 0.123 Repeating to a Fraction
To convert 0.123 repeating to a fraction, we can use the following steps:
- Let x = 0.123123... (where x is the repeating decimal)
- Multiply both sides of the equation by 1000 to get 1000x = 123.123123...
- Subtract the original equation from the new equation to get 999x = 123
- Divide both sides of the equation by 999 to get x = 123/999
Simplifying the Fraction
The fraction 123/999 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 123 and 999 is 41.
123 ÷ 41 = 3 999 ÷ 41 = 24
So, the simplified fraction is:
x = 3/24
Which can be further simplified to:
x = 1/8
Conclusion
In conclusion, the repeating decimal 0.123 repeating can be expressed as a simplified fraction, which is 1/8. This process can be applied to any repeating decimal to convert it into a simplified fraction.
