Explain in your own words:

Question

Why are numbers in expanded form with base 10 notation equal to the number itself for our number system

Answer 1

Numbers in expanded form with base 10 notation are equal to the number itself because our number system is based on powers of 10. In base 10, each digit's value is determined by its position in the number. The rightmost digit represents the units place, the next digit represents the tens place, and so on. When we expand a number in base 10, we break it down into the sum of its digit values multiplied by their respective powers of 10. Since each digit's value is calculated based on the position and the power of 10, when we add all these values together, we get the original number back. Therefore, numbers in expanded form with base 10 notation are equal to the number itself in our number system.