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Convert 40 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 >= 40

16⁰ = 1

16¹ = 16

16² = 256 <--- Stop: This is greater than 40

Since 256 is greater than 40, 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 40 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 <= 40, 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 40 is 8

Multiplying this coefficient by our original value, we get: 8 * 1 = 8

Add our new value to our running total, we get:
32 + 8 = 40

This = 40, so we assign our outside coefficient of 8 for this digit.

Our new sum becomes 40

Our hexadecimal notation is now equal to 28

Final Answer