.47 Repeating as a Fraction
What is .47 Repeating?
.47 repeating is a decimal number that has an infinite sequence of 47s. It can be written as:
.474747...
The sequence of 47s goes on forever, and it's a non-terminating, non-repeating decimal.
Converting .47 Repeating to a Fraction
To convert .47 repeating to a fraction, we can use a technique called the "repeating decimal to fraction" conversion.
Let's call .47 repeating as x. Since it's a repeating decimal, we can multiply both sides of the equation by 100 to get:
100x = 47.4747...
Now, subtract x from both sides of the equation to get:
99x = 47
Divide both sides of the equation by 99 to get:
x = 47/99
So, .47 repeating as a fraction is 47/99.
Simplifying the Fraction
We can simplify the fraction 47/99 by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 47 and 99 is 1, so the simplified fraction is still 47/99.
Conclusion
.47 repeating as a fraction is 47/99. This fraction is an exact conversion of the repeating decimal, and it can be used in mathematical calculations and applications.
