0.37 Repeating as a Fraction
Definition of a Repeating Decimal
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. For example, 0.37 repeating is a repeating decimal because the digits "37" repeat indefinitely.
Converting 0.37 Repeating to a Fraction
To convert 0.37 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.37 repeating
Let x = 0.37 repeating. This means that x = 0.373737...
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get:
100x = 37.3737...
Step 3: Subtract x from 100x
Subtract x from both sides of the equation to get:
99x = 37
Step 4: Divide by 99
Divide both sides of the equation by 99 to get:
x = 37/99
Therefore, 0.37 repeating as a fraction is 37/99.
Simplifying the Fraction
We can simplify the fraction 37/99 by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 37 and 99 is 1, so the simplified fraction is:
37/99
This is the simplest form of the fraction.
Conclusion
In conclusion, 0.37 repeating as a fraction is 37/99. By using the steps outlined above, we can convert any repeating decimal to a fraction.
