0.035 Repeating as a Fraction
In mathematics, a repeating decimal is a decimal representation of a number that recurs in a repeating pattern. One such example is 0.035, which is a repeating decimal. But have you ever wondered what 0.035 repeating as a fraction looks like?
Converting 0.035 Repeating to a Fraction
To convert 0.035 repeating to a fraction, we can follow these steps:
Step 1: Assign a Variable
Let's assign a variable x to the repeating decimal 0.035.
x = 0.035
Step 2: Multiply Both Sides by 100
Multiply both sides of the equation by 100 to get rid of the decimal point.
100x = 3.5
Step 3: Subtract the Original Equation
Subtract the original equation from the new equation to eliminate the x term.
100x - x = 3.5 - 0.035 99x = 3.465
Step 4: Divide by 99
Divide both sides of the equation by 99 to solve for x.
x = 3.465 / 99 x = 35 / 990 x = 7 / 198
And there you have it! The fraction equivalent of 0.035 repeating is 7 / 198.
Conclusion
In conclusion, 0.035 repeating as a fraction is equal to 7 / 198. This conversion is useful in various mathematical applications, such as algebra, geometry, and calculus, where fractions are often preferred over decimals.
