In our number system, also known as base 10 notation, each digit in a number represents a value based on its position in relation to the base. The base, in this case, is 10, meaning we have 10 digits (0-9) to represent all possible values.
When we write a number in expanded form with base 10 notation, we break it down into its individual digits and express each digit's value based on its position. For example, the number 342 is expressed as 300 + 40 + 2.
In this representation, each digit's value is determined by multiplying it with 10 raised to the power of its position. In the case of 342, we have 3 multiplied by 10^2 (which is 100), 4 multiplied by 10^1 (which is 10), and 2 multiplied by 10^0 (which is 1).
When we add these individual values together, we arrive at the original number, 342. This is because our base 10 system is designed in such a way that the sum of these individual values correctly represents the intended number. Thus, numbers in expanded form with base 10 notation equal the number itself in our number system.
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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