In our number system, which is based on the decimal system (base 10), each digit in a number holds a place value based on a power of 10. So, when we write a number in expanded form using base 10 notation, we are essentially breaking down the number into its individual digits and adding them according to their place values.
For example, let's take the number 843. In expanded form, we can write it as 8 * 100 + 4 * 10 + 3 * 1. This means that the 8 represents 800, the 4 represents 40, and the 3 represents 3. When we add up these three parts, we get 800 + 40 + 3, which is equal to the original number 843.
This is why numbers in expanded form with base 10 notation are equal to the number itself in our number system. Each digit's place value contributes to the final value, and when all the digits are added together, they represent the whole number.
xplain 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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