In our number system, which is known as base 10, each digit in a number carries a value based on its position. The position of each digit represents a power of 10. For example, in the number 352, the digit "3" represents 3 hundreds (10^2), the digit "5" represents 5 tens (10^1), and the digit "2" represents 2 ones (10^0).
When we write a number in expanded form, we decompose it into its individual digits and express each digit according to its place value. By doing so, we are essentially adding up the values of each digit to obtain the original number.
For instance, if we write the number 352 in expanded form, it would be expressed as 300 + 50 + 2. If we calculate this sum, we get 352, which is the original number. This is because each digit is multiplied by the corresponding power of 10, giving it the correct value within the number.
Therefore, numbers in expanded form with base 10 notation are equal to the number itself in our number system because we are representing the value of each digit according to its place value, which is determined by powers of 10.
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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