Put the steps In order for changing the repeating decimal which is rational to a ratio or fraction
To change a repeating decimal into a fractional or rational form, follow these steps:
1. Identify the repeating pattern: Look for a block of digits that repeats indefinitely. It is usually indicated by a bar placed over the repeating block.
2. Determine the number of digits in the repeating pattern: Count the number of digits in the repeating block. Let's call this number "n".
3. Assign variables to the repeating number: Let "x" represent the repeating block of digits.
4. Write an equation that represents the original decimal: Set up an equation to represent the original decimal by equating it to x.
5. Multiply both sides of the equation by a power of 10: Multiply both sides of the equation by 10^n, where n represents the number of digits in the repeating block.
6. Subtract the original equation from the equation obtained in step 5: Subtract the equation obtained in step 4 from the equation in step 5.
7. Solve the resulting equation: Simplify the equation obtained in step 6 and solve for x.
8. Express the decimal as a fraction: Write x as a fraction with the numerator equal to the solved value of x and the denominator equal to 10^n - 1.
9. Simplify the fraction if necessary: Check if the resulting fraction can be simplified further. If possible, divide the numerator and denominator by their greatest common divisor to simplify the fraction.
10. The resulting fraction is the rational form of the repeating decimal.
Note: In some cases, you may need to adjust the decimal point to obtain the correct value of x before proceeding with the steps.