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Convert 31 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 >= 31

8⁰ = 1

8¹ = 8

8² = 64 <--- Stop: This is greater than 31

Since 64 is greater than 31, we use 1 power less as our starting point which equals 1

Build octal notation

Work backwards from a power of 1

We start with a total sum of 0:

8¹ = 8

The highest coefficient less than 7 we can multiply this by to stay under 31 is 3

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

Add our new value to our running total, we get:
0 + 24 = 24

This is <= 31, so we assign our outside coefficient of 3 for this digit.

Our new sum becomes 24

Our octal notation is now equal to 3

8⁰ = 1

The highest coefficient less than 7 we can multiply this by to stay under 31 is 7

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

Add our new value to our running total, we get:
24 + 7 = 31

This = 31, so we assign our outside coefficient of 7 for this digit.

Our new sum becomes 31

Our octal notation is now equal to 37

Final Answer