Write the expanded form with base 10 notation.

Question

825.29

Write the expanded form with base 10 notation.
5.3257

Write the expanded form with base 10 notation.
0.45

Write the expanded form with base 10 notation.
125.325

Explain in your own words:
Why are numbers in expanded form with base 10 notation equal to the number itself for our number system?

Answer 1

In our number system (base 10), each digit in a number represents a multiple of a power of 10. For example, in the number 825.29, the "8" represents 8 hundreds (8 x 100), the "2" represents 2 tens (2 x 10), the "5" represents 5 ones (5 x 1), the "2" after the decimal point represents 2 tenths (2 x 0.1), and the "9" after the decimal point represents 9 hundredths (9 x 0.01). By adding up all these multiples of powers of 10, we get the original number. Therefore, the expanded form with base 10 notation is equal to the number itself in our number system.