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Convert 57 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 >= 57

8⁰ = 1

8¹ = 8

8² = 64 <--- Stop: This is greater than 57

Since 64 is greater than 57, 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 57 is 7

Multiplying this coefficient by our original value, we get: 7 * 8 = 56

Add our new value to our running total, we get:
0 + 56 = 56

This is <= 57, so we assign our outside coefficient of 7 for this digit.

Our new sum becomes 56

Our octal notation is now equal to 7

8⁰ = 1

The highest coefficient less than 7 we can multiply this by to stay under 57 is 1

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

Add our new value to our running total, we get:
56 + 1 = 57

This = 57, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 57

Our octal notation is now equal to 71

Final Answer