Converting 0.175 Repeating to a Fraction in Simplest Form
In mathematics, repeating decimals can be converted into fractions in simplest form. In this article, we will explore how to convert 0.175 repeating to a fraction in simplest form.
What is 0.175 Repeating?
0.175 repeating is a decimal number that has a repeating pattern of 175. The repetition can be denoted by a horizontal line above the repeating digits. In this case, the decimal can be written as:
0.175̄
Converting 0.175 Repeating to a Fraction
To convert 0.175 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.175̄
Let x be equal to the given decimal number.
Step 2: Multiply x by 1000
Multiply both sides of the equation by 1000 to get rid of the decimal points.
1000x = 175.175̄
Step 3: Subtract x from both sides
Subtract x from both sides of the equation to get:
999x = 175
Step 4: Divide both sides by 999
Divide both sides of the equation by 999 to solve for x.
x = 175/999
Step 5: Simplify the fraction
The fraction 175/999 is already in simplest form. Therefore, we can write:
0.175̄ = 175/999
Conclusion
In conclusion, the decimal number 0.175 repeating can be converted to a fraction in simplest form as 175/999. This method can be applied to convert any repeating decimal to a fraction in simplest form.
