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Convert 7 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 >= 7

8⁰ = 1

8¹ = 8 <--- Stop: This is greater than 7

Since 8 is greater than 7, we use 1 power less as our starting point which equals 0

Build octal notation

Work backwards from a power of 0

We start with a total sum of 0:

8⁰ = 1

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

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

Add our new value to our running total, we get:
0 + 7 = 7

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

Our new sum becomes 7

Our octal notation is now equal to 7

Final Answer