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Convert 117 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 >= 117

8⁰ = 1

8¹ = 8

8² = 64

8³ = 512 <--- Stop: This is greater than 117

Since 512 is greater than 117, 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 117 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 <= 117, 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 117 is 6

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

Add our new value to our running total, we get:
64 + 48 = 112

This is <= 117, so we assign our outside coefficient of 6 for this digit.

Our new sum becomes 112

Our octal notation is now equal to 16

8⁰ = 1

The highest coefficient less than 7 we can multiply this by to stay under 117 is 5

Multiplying this coefficient by our original value, we get: 5 * 1 = 5

Add our new value to our running total, we get:
112 + 5 = 117

This = 117, so we assign our outside coefficient of 5 for this digit.

Our new sum becomes 117

Our octal notation is now equal to 165

Final Answer