Base 5, also known as quinary, is a number system that uses five symbols to represent numbers. The five symbols used in base 5 number system are 0, 1, 2, 3, and 4. In this number system, every digit within a number has a base 5 value, which is five times greater than the digit to its right. This means that the base 5 representation of a number is obtained by multiplying each of its digits by the appropriate power of 5 and then summing up all the resulting values.

To find the base 5 representation of the number 219, we need to first break it down into its individual digits, which are 2, 1, and 9. Now we can calculate the base 5 representation of each of these digits by multiplying them with the appropriate power of 5. Since the rightmost digit is 9, it remains the same. The next one is 1, which is multiplied by 5 to get 5. Finally, the leftmost digit 2 is multiplied by 25 to get 50.

Now we can add all these values to get the base 5 representation of the number 219, which is 54. This means that the base 5 representation of the number 219 is 54. It can also be written as 5 x 25 + 4 x 5 + 9.

The base 5 representation of a number can be used for representing large numbers in a shorter form. It is also useful for performing computations in base 5 number system. For example, if we want to add two base 5 numbers, we can first convert them into base 10 numbers and then add them using the standard addition procedure. After the addition is performed, we can then convert the result back into base 5.

## Conclusion

In conclusion, the base 5 representation of the number 219 is 54. This can be obtained by multiplying each of the individual digits with the appropriate power of 5 and then summing up the resulting values. Base 5 representation of a number can be used to represent large numbers in a shorter form and it is also useful for performing computations in base 5 number system.

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