0.02 Recurring as a Fraction
The decimal number 0.02 recurring, also written as 0.02~, is a repeating decimal that has a specific pattern. In this article, we will explore what this decimal number represents as a fraction.
What is a Recurring Decimal?
A recurring decimal, also known as a repeating decimal, is a decimal number that has a sequence of digits that repeats indefinitely. For example, 0.12341234... is a recurring decimal because the sequence "1234" repeats over and over again.
Converting 0.02 Recurring to a Fraction
To convert 0.02 recurring to a fraction, we can use the following steps:
- Let x = 0.02~
- Multiply both sides by 100 to eliminate the decimal point: 100x = 2.02~
- Subtract the original equation from the new equation: 99x = 2
- Divide both sides by 99: x = 2/99
Therefore, 0.02 recurring can be written as a fraction as:
2/99
Simplifying the Fraction
We can simplify the fraction 2/99 by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 2 and 99 is 1, so the fraction remains the same:
2/99
In conclusion, the decimal number 0.02 recurring can be written as a fraction in its simplest form as 2/99.
