Question

0.27 repeating as a fraction

Answer 1

To express the repeating decimal 0.27 as a fraction, we can follow these steps:

Step 1: Let x = 0.27 (repeating decimal).
Step 2: Multiply both sides of the equation by 100 (since there are two decimal places):
100x = 27.27 (this helps us eliminate the repeating decimal).
Step 3: Subtract the original equation from the new equation to eliminate the repeating decimal:
100x - x = 27.27 - 0.27
99x = 27
Step 4: Divide both sides of the equation by 99:
x = 27/99

Therefore, the repeating decimal 0.27 can be expressed as the fraction 27/99, which can be simplified to 3/11.