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Convert 223 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 >= 223

8⁰ = 1

8¹ = 8

8² = 64

8³ = 512 <--- Stop: This is greater than 223

Since 512 is greater than 223, 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 223 is 3

Multiplying this coefficient by our original value, we get: 3 * 64 = 192

Add our new value to our running total, we get:
0 + 192 = 192

This is <= 223, so we assign our outside coefficient of 3 for this digit.

Our new sum becomes 192

Our octal notation is now equal to 3

8¹ = 8

The highest coefficient less than 7 we can multiply this by to stay under 223 is 3

Multiplying this coefficient by our original value, we get: 3 * 8 = 24

Add our new value to our running total, we get:
192 + 24 = 216

This is <= 223, so we assign our outside coefficient of 3 for this digit.

Our new sum becomes 216

Our octal notation is now equal to 33

8⁰ = 1

The highest coefficient less than 7 we can multiply this by to stay under 223 is 7

Multiplying this coefficient by our original value, we get: 7 * 1 = 7

Add our new value to our running total, we get:
216 + 7 = 223

This = 223, so we assign our outside coefficient of 7 for this digit.

Our new sum becomes 223

Our octal notation is now equal to 337

Final Answer