0.0370 Repeating as a Fraction
The decimal 0.0370 repeating can be written as a fraction by using the following steps:
Step 1: Identify the repeating part
The repeating part of the decimal is 0370. To identify this, we can look for the sequence of digits that repeat: 0370, 0370, 0370, and so on.
Step 2: Let x = the decimal
Let x = 0.0370 repeating.
Step 3: Multiply both sides by 10,000
Multiply both sides of the equation by 10,000 to get:
10,000x = 370.0370...
Step 4: Subtract the original equation
Subtract the original equation from the new equation:
10,000x - x = 370.0370... - 0.0370...
Step 5: Simplify the equation
Simplify the equation by combining like terms:
9,999x = 370
Step 6: Divide both sides by 9,999
Divide both sides of the equation by 9,999 to get:
x = 370/9,999
The answer
So, 0.0370 repeating as a fraction is equal to:
370/9,999
This fraction can be simplified further by dividing both the numerator and the denominator by their greatest common divisor, which is 1. Therefore, the simplified fraction is:
370/9,999
