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Convert 457 from decimal to hexadecimal (base 16) notation:

Start by raising our base of 16 to a power starting at 0 and increasing by 1 until it is >= 457
160 = 1
161 = 16
162 = 256
163 = 4096 <--- Stop: This is greater than 457

Since 4096 is greater than 457, we use 1 power less as our starting point which equals 2.

Now start building our hexadecimal notation working backwards from a power of 2.

162 = 256.
The highest coefficient less than 15 we can multiply this by to stay under 457 is 1.
Multiplying this coefficient by our original value, we get: 1 * 256 = 256.
Adding our new value to our running total, we get: 0 + 256 = 256.

This is <= 457, so we assign our outside coefficient of 1 for this digit.
Our new sum becomes 256.
Our hexadecimal notation is now equal to 1

161 = 16.
The highest coefficient less than 15 we can multiply this by to stay under 457 is 12.
Multiplying this coefficient by our original value, we get: 12 * 16 = 192.
Adding our new value to our running total, we get: 256 + 192 = 448.

Hexadecimal (10 - 15) are represented by an (A-F) where 12 translates to the letter C.
This is <= 457, so we assign our outside coefficient of C for this digit.
Our new sum becomes 448.
Our hexadecimal notation is now equal to 1C

160 = 1.
The highest coefficient less than 15 we can multiply this by to stay under 457 is 9.
Multiplying this coefficient by our original value, we get: 9 * 1 = 9.
Adding our new value to our running total, we get: 448 + 9 = 457.

This = 457, so we assign our outside coefficient of 9 for this digit.
Our new sum becomes 457.
Our hexadecimal notation is now equal to 1C9

We are done. 457 converted from decimal to hexadecimal notation equals 1C916.