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Convert 47 from decimal to hexadecimal

(base 16) notation:

##### Power Test

Raise our base of 16 to a power

Start at 0 and increasing by 1 until it is >= 47

160 = 1

161 = 16

162 = 256 <--- Stop: This is greater than 47

Since 256 is greater than 47, we use 1 power less as our starting point which equals 1

##### Build hexadecimal notation

Work backwards from a power of 1

We start with a total sum of 0:

##### 161 = 16

The highest coefficient less than 15 we can multiply this by to stay under 47 is 2

Multiplying this coefficient by our original value, we get: 2 * 16 = 32

Add our new value to our running total, we get:
0 + 32 = 32

This is <= 47, so we assign our outside coefficient of 2 for this digit.

Our new sum becomes 32

Our hexadecimal notation is now equal to 2

##### 160 = 1

The highest coefficient less than 15 we can multiply this by to stay under 47 is 15

Multiplying this coefficient by our original value, we get: 15 * 1 = 15

Add our new value to our running total, we get:
32 + 15 = 47

Hexadecimal (10 - 15) are represented by an (A-F) where 15 translates to the letter F

This = 47, so we assign our outside coefficient of F for this digit.

Our new sum becomes 47

Our hexadecimal notation is now equal to 2F

##### Final Answer

We are done. 47 converted from decimal to hexadecimal notation equals 2F16.

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