2. Repeating Decimal to a fraction - RATIONAL
To convert a repeating decimal to a fraction, we can follow these steps:
Step 1: Identify the repeating portion of the decimal.
Step 2: Let x be the repeating portion.
Step 3: Multiply both sides of the equation x = 0.abcdef... by 10^n, where n is the number of digits in the repeating portion.
Step 4: Subtract the equation from Step 2 from the equation in Step 3.
Step 5: Solve for x.
Step 6: Convert x to a fraction by writing it as x/1.
Step 7: Simplify the fraction.
Let's take an example to illustrate the process:
Example: Convert the decimal 0.777... to a fraction.
Step 1: The repeating portion of the decimal is 7.
Step 2: Let x = 0.777...
Step 3: Multiply both sides by 10: 10x = 7.777...
Step 4: Subtract the equation from Step 2 from the equation in Step 3: 10x - x = 7.777... - 0.777... => 9x = 7
Step 5: Solve for x: x = 7/9
Step 6: Convert x to a fraction: x = 7/9
Step 7: The fraction is already in simplest form, so the final answer is 7/9.
Therefore, the decimal 0.777... can be expressed as the fraction 7/9.