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Convert 42 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 >= 42

8⁰ = 1

8¹ = 8

8² = 64 <--- Stop: This is greater than 42

Since 64 is greater than 42, 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 42 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 <= 42, 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 42 is 2

Multiplying this coefficient by our original value, we get: 2 * 1 = 2

Add our new value to our running total, we get:
40 + 2 = 42

This = 42, so we assign our outside coefficient of 2 for this digit.

Our new sum becomes 42

Our octal notation is now equal to 52

Final Answer