0.152 Repeating as a Fraction
The decimal value 0.152 repeating can be converted into a fraction. To do this, we need to identify the repeating pattern in the decimal and then perform some calculations.
Identifying the Repeating Pattern
The decimal value 0.152 repeating can be written as 0.15252525..., where the pattern "52" repeats indefinitely. This is a key characteristic of a repeating decimal.
Converting to a Fraction
To convert 0.152 repeating to a fraction, we can use the following steps:
Let x = 0.15252525...
Multiply both sides by 100 to get:
100x = 15.252525...
Subtract x from both sides to eliminate the repeating pattern:
100x - x = 15.252525... - 0.15252525...
This simplifies to:
99x = 15.1
Divide both sides by 99:
x = 15.1/99
Simplifying the Fraction
The fraction 15.1/99 can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD). The GCD of 15.1 and 99 is 9.9, which simplifies to 1.
So, the simplified fraction is:
x = 151/990
Final Answer
The decimal value 0.152 repeating as a fraction is 151/990.
