Final answer:
Each digit has a different value because our numbering system is based on powers of ten. The value of a digit is determined by its position in the number. In exponential notation, the exponent indicates the number of places the decimal point is shifted.
Step-by-step explanation:
The reason each digit has a different value is because our numbering system is based on powers of ten. Each place in our numbering system is ten times greater than the place to the right of it. For example, in the number 123, the digit 1 represents 100 (10 times as large as the ones place), the digit 2 represents 20 (10 times as large as the tens place), and the digit 3 represents 3 (10 times as large as the hundreds place).
This can be better understood using the concept of exponential notation. When we write a number in scientific notation like 1.23 x 10^2, we are saying that the number is equal to 1.23 multiplied by 10 raised to the power of 2. In this case, the exponent 2 indicates that the decimal point is shifted two places to the right, making the number 100 times larger than 1.23.
In contrast, when we have a number like 0.0123 x 10^-2, the exponent -2 indicates that the decimal point is shifted two places to the left, making the number 100 times smaller than 0.0123. Each digit in a number has a different value because it represents a different power of ten in our numbering system.