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Convert 41 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 >= 41

8⁰ = 1

8¹ = 8

8² = 64 <--- Stop: This is greater than 41

Since 64 is greater than 41, 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 41 is 5

Multiplying this coefficient by our original value, we get: 5 * 8 = 40

Add our new value to our running total, we get:
0 + 40 = 40

This is <= 41, so we assign our outside coefficient of 5 for this digit.

Our new sum becomes 40

Our octal notation is now equal to 5

8⁰ = 1

The highest coefficient less than 7 we can multiply this by to stay under 41 is 1

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

Add our new value to our running total, we get:
40 + 1 = 41

This = 41, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 41

Our octal notation is now equal to 51

Final Answer