0.004 Recurring as a Fraction in Simplest Form
What is a Recurring Decimal?
A recurring decimal is a decimal number that has a sequence of digits that repeats indefinitely. For example, 0.004 is a recurring decimal because the digits "004" repeat indefinitely.
Converting 0.004 Recurring to a Fraction
To convert 0.004 recurring to a fraction, we can use the following steps:
Let x = 0.004004004...
Multiply both sides by 1000 to get:
1000x = 4.004004...
Subtract the original equation from the new equation to get:
999x = 4
Divide both sides by 999 to get:
x = 4/999
Simplifying the Fraction
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 4 and 999 is 1, so the simplified fraction is:
x = 4/999
Therefore, 0.004 recurring can be written as a fraction in simplest form as 4/999.
