0.005 Repeating as a Fraction
In mathematics, repeating decimals can be converted to fractions by applying a simple formula. In this article, we will explore how to convert 0.005 repeating to a fraction.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, 0.005 is a repeating decimal because the sequence "005" repeats indefinitely: 0.005, 0.005005, 0.005005005, and so on.
Converting 0.005 Repeating to a Fraction
To convert 0.005 repeating to a fraction, we can use the following formula:
x = 0.005(repeating)
1000x = 5.005(repeating)
Notice that multiplying both sides by 1000 (which is 10^3, since the repeating sequence has 3 digits) eliminates the decimal part, leaving us with a whole number.
Subtracting the Original Equation
Now, let's subtract the original equation from the new equation:
1000x - x = 5.005 - 0.005
This simplifies to:
999x = 5
Dividing Both Sides by 999
Finally, we can divide both sides by 999 to solve for x:
x = 5/999
So, 0.005 repeating as a fraction is 5/999.
Conclusion
In conclusion, converting 0.005 repeating to a fraction is a simple process that involves multiplying the original equation by a power of 10, subtracting the original equation, and dividing by the resulting coefficient. The result is a fraction that represents the repeating decimal: 5/999.
