0.0222 Repeating as a Fraction
The decimal number 0.0222 is a repeating decimal, where the sequence "22" repeats indefinitely. To convert this repeating decimal to a fraction, we can use a few different methods.
Method 1: Using the Formula
One way to convert a repeating decimal to a fraction is to use the following formula:
a = d/99
where a is the repeating decimal and d is the number formed by the repeating digits.
In this case, the repeating decimal is 0.0222, so we can plug in the values as follows:
a = 0.0222 d = 22
Substituting these values into the formula, we get:
0.0222 = 22/99
Method 2: Using Equations
Another way to convert a repeating decimal to a fraction is to set up an equation based on the repeating pattern.
Let's say the repeating decimal is equal to x:
x = 0.0222
We can multiply both sides of the equation by 100 to get:
100x = 2.22
Since the decimal repeats, we know that the decimal part of 100x is the same as the decimal part of x. Therefore, we can set up the following equation:
100x - x = 2.22 - 0.0222
Simplifying this equation, we get:
99x = 2.2
Dividing both sides by 99, we get:
x = 2.2/99
x = 22/99
Simplifying the Fraction
The fraction 22/99 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 22 and 99 is 11, so we can divide both numbers by 11 to get:
22 ÷ 11 = 2 99 ÷ 11 = 9
Therefore, the simplified fraction is:
x = 2/9
So, the repeating decimal 0.0222 is equal to the fraction 2/9.
