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Convert 272 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 >= 272

80 = 1

81 = 8

82 = 64

83 = 512 <--- Stop: This is greater than 272

Since 512 is greater than 272, 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 272 is 4

Multiplying this coefficient by our original value, we get: 4 * 64 = 256

Add our new value to our running total, we get:
0 + 256 = 256

This is <= 272, so we assign our outside coefficient of 4 for this digit.

Our new sum becomes 256

Our octal notation is now equal to 4


81 = 8

The highest coefficient less than 7 we can multiply this by to stay under 272 is 2

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

Add our new value to our running total, we get:
256 + 16 = 272

This = 272, so we assign our outside coefficient of 2 for this digit.

Our new sum becomes 272

Our octal notation is now equal to 42


80 = 1

The highest coefficient less than 7 we can multiply this by to stay under 272 is 1

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

Add our new value to our running total, we get:
272 + 1 = 273

This is > 272, so we assign a 0 for this digit.

Our total sum remains the same at 272

Our octal notation is now equal to 420


Final Answer


We are done. 272 converted from decimal to octal notation equals 4208.