The decimal point of a positive real number is moved two digits to the right to form a different real number. When the positive
difference between these two real numbers is divided by 11, the answer is 21. What is the original real number? Express your answer as a common fraction.
Step-by-step explanation: let the original real number be x. After moving the decimal point of this real number two digits to the right, the number becomes 100x. The positive difference between the two numbers is 100x - x = 99x. Dividing the difference by 11, we have 99x/11 = 9x, which we are told is 21, so we have the equation 9x = 21/9, which equals 7/3. Thus, the original real number is 7/3.
