convert the repeating decimal to a/b where a,b are integers and b #0.
Express the recurring decimal 1.6333... in the form a/b where a and b are integers.
To convert a repeating decimal to a fraction, you can follow these steps:
Step 1: Let x be the repeating decimal.
Step 2: Multiply both sides of the equation by a power of 10 such that all the repeating digits are to the left of the decimal point. This step ensures that we can subtract the original equation from the expanded equation, eliminating the repeating part.
Step 3: Let y be the resulting number after performing step 2.
Step 4: Subtract the equation in step 1 from the equation in step 3 to eliminate the repeating part.
Step 5: Solve the resulting equation for y to find the value of y.
Step 6: Express y as a fraction in the form a/b, where a is the resulting value of y obtained in step 5, and b is a power of 10 representing the number of decimal places in the repeating part.
For example, let's convert the repeating decimal 0.777... to a fraction:
Step 1: Let x = 0.777...
Step 2:
Multiply both sides by 10 since there is one repeating digit to the right of the decimal point: 10x = 7.777...
Step 3: Let y = 10x = 7.777...
Step 4: Subtract the equation in step 1 from the equation in step 3: 10x - x = 7.777... - 0.777...
Simplifying, we get: 9x = 7
Step 5: Solve the equation for x: x = 7/9
Step 6: Express x as a fraction in the form a/b: 0.777... = 7/9
So, the repeating decimal 0.777... can be written as the fraction 7/9.