Pick any single digit number. Multipy it by 12,345,679. Then multiply the result by 9. What happens? Explain why this works.
When you pick any single-digit number and multiply it by 12,345,679, and then multiply the result by 9, something interesting happens. The outcome will always be a repeating number pattern consisting of all the single digits, starting from 1 and ending with 9.
For example, let's say we choose the number 3. We multiply it by 12,345,679, which gives us 37,037,037. Now, if we multiply this result by 9, we get 333,333,333. As you can see, the repeating pattern of digits from 1 to 9 appears.
To understand why this works, we need to explore the properties of the number 12,345,679. This number is a special case of a cyclic number, meaning it exhibits a particular pattern when multiplied by different numbers. In the case of 12,345,679, when it is multiplied by any single-digit number (from 0 to 9), it generates a cyclic pattern.
Multiplying any single-digit number by a cyclic number essentially redistributes the digits. When we multiply by 9, the cyclic pattern of 12,345,679 is replicated nine times in a row. This repetition ensures that every digit from 1 to 9 appears in the final result, forming the repeating pattern.
In summary, multiplying any single-digit number by 12,345,679 and then multiplying the result by 9 generates a repeating sequence of digits from 1 to 9. This is due to the unique cyclic property of 12,345,679.