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Write the repeating decimal as a fraction.
Full solution
Q. Write the repeating decimal as a fraction.
- Identify Repeating Pattern: Let's identify the repeating pattern in the decimal. The digits repeat indefinitely.
- Convert to Fraction: To convert the repeating decimal to a fraction, let's denote the repeating decimal as :
- Isolate Repeating Part: To isolate the repeating part, we can multiply by , since there are three digits in the repeating sequence:
- Subtract Decimal Part: Now, we subtract the original from to get rid of the decimal part:
- Solve for x: Performing the subtraction, we get:
- Simplify Fraction: Now, we solve for by dividing both sides of the equation by :
- Simplify Fraction: Now, we solve for by dividing both sides of the equation by :We can simplify the fraction by looking for a common divisor. Both and are divisible by , but we need to check if there's a larger common divisor to simplify the fraction further.
- Simplify Fraction: Now, we solve for by dividing both sides of the equation by :We can simplify the fraction by looking for a common divisor. Both and are divisible by , but we need to check if there's a larger common divisor to simplify the fraction further.Upon checking, we find that there is no common divisor greater than for and . Therefore, the fraction is already in its simplest form.
