1) Write the expanded form with base 10 notation.
825.29
2) Write the expanded form with base 10 notation.
5.3257
3) Write the expanded form with base 10 notation.
0.45
4) Write the expanded form with base 10 notation.
125.325
5) Explain in your own words:
Why are numbers in expanded form with base 10 notation equal to the number itself for our number system?
1) The expanded form of 825.29 in base 10 notation is: (8 x 10^2) + (2 x 10^1) + (5 x 10^0) + (2 x 10^-1) + (9 x 10^-2).
2) The expanded form of 5.3257 in base 10 notation is: (5 x 10^0) + (3 x 10^-1) + (2 x 10^-2) + (5 x 10^-3) + (7 x 10^-4).
3) The expanded form of 0.45 in base 10 notation is: (4 x 10^-1) + (5 x 10^-2).
4) The expanded form of 125.325 in base 10 notation is: (1 x 10^2) + (2 x 10^1) + (5 x 10^0) + (3 x 10^-1) + (2 x 10^-2) + (5 x 10^-3).
5) In our number system, base 10, each digit of a number is multiplied by the corresponding power of 10. This is because we use a decimal system that is based on powers of 10. For example, the number 825.29 can be represented as (8 x 10^2) + (2 x 10^1) + (5 x 10^0) + (2 x 10^-1) + (9 x 10^-2). The power of 10 indicates the position of the digit in the number, and multiplying the digit by the respective power of 10 gives its value in the overall number. Therefore, the expanded form in base 10 notation for a number is equal to the number itself in our number system.