Express 0.bar(245) as a Fraction in Simplest Form
In mathematics, a repeating decimal can be expressed as a fraction. In this article, we will explore how to express 0.bar(245) as a fraction in its simplest form.
What is 0.bar(245)?
0.bar(245) is a repeating decimal where the digits "245" repeat indefinitely. It can be written as:
0.245245245...
Converting 0.bar(245) to a Fraction
To convert 0.bar(245) to a fraction, we can use the following steps:
Step 1: Let x = 0.bar(245)
Let x = 0.245245245...
Step 2: Multiply x by 1000
Multiply both sides of the equation by 1000 to get:
1000x = 245.245245...
Step 3: Subtract x from 1000x
Subtract x from 1000x to eliminate the repeating decimal part:
1000x - x = 245.245245... - 0.245245245... 999x = 245
Step 4: Divide by 999
Divide both sides of the equation by 999:
x = 245/999
Simplifying the Fraction
The fraction 245/999 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 245 and 999 is 1, so the fraction is already in its simplest form:
x = 245/999
Therefore, 0.bar(245) can be expressed as a fraction in its simplest form as:
0.bar(245) = 245/999
This fraction represents the repeating decimal 0.245245245... in its simplest form.
