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Convert 52 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 >= 52

8⁰ = 1

8¹ = 8

8² = 64 <--- Stop: This is greater than 52

Since 64 is greater than 52, 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 52 is 6

Multiplying this coefficient by our original value, we get: 6 * 8 = 48

Add our new value to our running total, we get:
0 + 48 = 48

This is <= 52, so we assign our outside coefficient of 6 for this digit.

Our new sum becomes 48

Our octal notation is now equal to 6

8⁰ = 1

The highest coefficient less than 7 we can multiply this by to stay under 52 is 4

Multiplying this coefficient by our original value, we get: 4 * 1 = 4

Add our new value to our running total, we get:
48 + 4 = 52

This = 52, so we assign our outside coefficient of 4 for this digit.

Our new sum becomes 52

Our octal notation is now equal to 64

Final Answer