In our number system, each digit in a number represents a certain value based on its position. The position of a digit determines its place value, which is determined by powers of 10. For example, in the number 587, the digit 5 represents 5 hundreds, the digit 8 represents 8 tens, and the digit 7 represents 7 ones.
When we write a number in expanded form with base 10 notation, we break down the number into its individual digits and expand each digit according to its place value. By doing this, we are essentially expressing the number as a sum of its digit values.
Since each digit is multiplied by the corresponding power of 10, when we add up all the digit values, we obtain the original number itself. For example, 5 hundreds (500) plus 8 tens (80) plus 7 ones (7) equals 587, which is the original number.
This is why numbers in expanded form with base 10 notation equal the number itself in our number system, as each digit's value is added together to obtain the original number.
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?
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