Question

Does all digits in 9,999,999 have the same value? What is the relationship between the values of the digits in the number.

Answer 1

Yes, all digits in the number 9,999,999 have the same value. In this case, each digit is the same: the digit '9'.

The relationship between the values of the digits in the number can be described as follows:

- Each digit contributes equally to the overall value of the number.
- Since each digit is 9, the total value of the number is derived from the position (or place value) of each digit.

The places from right to left in a number represent increasing powers of 10:

- The rightmost '9' is in the 10^0 (units) place,
- The next '9' is in the 10^1 (tens) place,
- The next is in the 10^2 (hundreds) place,
- The next is in the 10^3 (thousands) place,
- The next is in the 10^4 (ten thousands) place,
- The next is in the 10^5 (hundred thousands) place,
- The leftmost '9' is in the 10^6 (millions) place.

Therefore, 9,999,999 can be expanded as follows:

\[
9 \times 10^6 + 9 \times 10^5 + 9 \times 10^4 + 9 \times 10^3 + 9 \times 10^2 + 9 \times 10^1 + 9 \times 10^0
\]

When summed together, this gives you the total value of the number, which is 9,999,999.

In summary, each digit has the same value (9), but their contributions to the overall value of the number vary based on their place value.