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Convert 67 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 >= 67

8⁰ = 1

8¹ = 8

8² = 64

8³ = 512 <--- Stop: This is greater than 67

Since 512 is greater than 67, we use 1 power less as our starting point which equals 2

Build octal notation

Work backwards from a power of 2

We start with a total sum of 0:

8² = 64

The highest coefficient less than 7 we can multiply this by to stay under 67 is 1

Multiplying this coefficient by our original value, we get: 1 * 64 = 64

Add our new value to our running total, we get:
0 + 64 = 64

This is <= 67, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 64

Our octal notation is now equal to 1

8¹ = 8

The highest coefficient less than 7 we can multiply this by to stay under 67 is 1

Multiplying this coefficient by our original value, we get: 1 * 8 = 8

Add our new value to our running total, we get:
64 + 8 = 72

This is > 67, so we assign a 0 for this digit.

Our total sum remains the same at 64

Our octal notation is now equal to 10

8⁰ = 1

The highest coefficient less than 7 we can multiply this by to stay under 67 is 3

Multiplying this coefficient by our original value, we get: 3 * 1 = 3

Add our new value to our running total, we get:
64 + 3 = 67

This = 67, so we assign our outside coefficient of 3 for this digit.

Our new sum becomes 67

Our octal notation is now equal to 103

Final Answer