0.510 Repeating as a Fraction
The decimal number 0.510 repeating, also written as 0.510..., is a non-terminating repeating decimal. In this article, we will explore how to convert this decimal number into a fraction.
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 0.510 repeating, the sequence "510" repeats indefinitely.
Converting 0.510 Repeating to a Fraction
To convert 0.510 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.510...
Let x = 0.510... (1)
Step 2: Multiply both sides by 1000
Since the repeating sequence is 3 digits long, we multiply both sides of the equation by 1000 to shift the decimal point 3 places to the right.
1000x = 510.510... (2)
Step 3: Subtract Equation (1) from Equation (2)
Subtracting Equation (1) from Equation (2), we get:
999x = 510
Step 4: Solve for x
Dividing both sides of the equation by 999, we get:
x = 510/999
Result
So, 0.510 repeating as a fraction is equal to:
510/999
Therefore, the fraction equivalent of 0.510 repeating is 510/999.
Conclusion
In conclusion, we have successfully converted 0.510 repeating to a fraction, which is equal to 510/999. This method can be applied to any repeating decimal to convert it into a fraction.
