Question

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

Answer 1

[AI-generated answer — Bot GPT 3.5]

In our number system, which is known as the base-10 or decimal system, each digit in a number represents a multiple of a power of 10. The base-10 system uses ten different digits (0-9) to represent numbers.

When we write a number in expanded form with base-10 notation, we break down the number into its individual digits and express each digit as a multiple of a power of 10. The value of each digit is determined by its position in the number.

For example, let's take the number 456. In expanded form with base-10 notation, it can be written as:

4 x 100 + 5 x 10 + 6 x 1

Here, the digit 4 is in the hundreds position, so it is multiplied by 100 (10^2). The digit 5 is in the tens position, so it is multiplied by 10 (10^1). The digit 6 is in the ones position, so it is multiplied by 1 (10^0).

When we simplify this expression, we get:

400 + 50 + 6 = 456

So, the number 456 expressed in expanded form with base-10 notation is equal to the number itself.

This is because our number system is based on powers of 10. Each digit's value depends on its position, which determines the power of 10 it is multiplied by. By adding up these multiplied values, we obtain the original number.