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Convert 150 from decimal to octal

(base 8) notation:

Power Test

Raise our base of 8 to a power

Start at 0 and increasing by 1 until it is >= 150

80 = 1

81 = 8

82 = 64

83 = 512 <--- Stop: This is greater than 150

Since 512 is greater than 150, we use 1 power less as our starting point which equals 2

Build octal notation

Work backwards from a power of 2

We start with a total sum of 0:


82 = 64

The highest coefficient less than 7 we can multiply this by to stay under 150 is 2

Multiplying this coefficient by our original value, we get: 2 * 64 = 128

Add our new value to our running total, we get:
0 + 128 = 128

This is <= 150, so we assign our outside coefficient of 2 for this digit.

Our new sum becomes 128

Our octal notation is now equal to 2


81 = 8

The highest coefficient less than 7 we can multiply this by to stay under 150 is 2

Multiplying this coefficient by our original value, we get: 2 * 8 = 16

Add our new value to our running total, we get:
128 + 16 = 144

This is <= 150, so we assign our outside coefficient of 2 for this digit.

Our new sum becomes 144

Our octal notation is now equal to 22


80 = 1

The highest coefficient less than 7 we can multiply this by to stay under 150 is 6

Multiplying this coefficient by our original value, we get: 6 * 1 = 6

Add our new value to our running total, we get:
144 + 6 = 150

This = 150, so we assign our outside coefficient of 6 for this digit.

Our new sum becomes 150

Our octal notation is now equal to 226


Final Answer


We are done. 150 converted from decimal to octal notation equals 2268.