The Place Value Problem
Dr. Sunita Verma was explaining the elegance of the Hindu number system to her students, noting that the same numeral can hold vastly different values depending on its position. She wrote a seemingly simple number on the board: \(7,007\). She challenged the class to analyze this number, highlighting how the placeholders (the zeros) and the position of the two fives showcase the system's efficiency. Understanding this fundamental concept is crucial, she stressed, because it is the key reason why this system is considered one of history's greatest mathematical inventions and why it enables unambiguous writing and easy computation.
Consider the Hindu number \(7,007\)
(i) What is the place value of the leftmost digit 7?
(ii) What is the actual value of the rightmost digit 7?
(iii) What is the actual value of the digit \(0\)?
(iv) How many times greater is the value of the leftmost 7 than the value of the rightmost 7?