The first steps to understanding Why multiplication works is understanding what a multiple digit integer really is. You have been working with integers for so long that this understanding is intuitive. In the decimal system each digit represents a different power of 10. The integer 1 is equal to 10 to the power of 0, integer 10 is equal to 10 to the power of 1, integer 100 is equal to 10 to the power of 2, integer 1000 is equal to 10 to the power of 3, and so on. All of the examples in the above paragraph refer to integers that include only the digit 1. What would the integer 500 equal using powers of 10? How did you come up with that answer?

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The first steps to understanding Why multiplication works is understanding what a multiple digit integer really is. You have been working with integers for so long that this understanding is intuitive. In the decimal system each digit represents a different power of 10. The integer 1 is equal to 10 to the power of 0, integer 10 is equal to 10 to the power of 1, integer 100 is equal to 10 to the power of 2, integer 1000 is equal to 10 to the power of 3, and so on. All of the examples in the above paragraph refer to integers that include only the digit 1. What would the integer 500 equal using powers of 10? How did you come up with that answer?
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