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Convert 157 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 >= 157

8⁰ = 1

8¹ = 8

8² = 64

8³ = 512 <--- Stop: This is greater than 157

Since 512 is greater than 157, 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 157 is 2

Multiplying this coefficient by our original value, we get: 2 * 64 = 128

Add our new value to our running total, we get:
0 + 128 = 128

This is <= 157, so we assign our outside coefficient of 2 for this digit.

Our new sum becomes 128

Our octal notation is now equal to 2

8¹ = 8

The highest coefficient less than 7 we can multiply this by to stay under 157 is 3

Multiplying this coefficient by our original value, we get: 3 * 8 = 24

Add our new value to our running total, we get:
128 + 24 = 152

This is <= 157, so we assign our outside coefficient of 3 for this digit.

Our new sum becomes 152

Our octal notation is now equal to 23

8⁰ = 1

The highest coefficient less than 7 we can multiply this by to stay under 157 is 5

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

Add our new value to our running total, we get:
152 + 5 = 157

This = 157, so we assign our outside coefficient of 5 for this digit.

Our new sum becomes 157

Our octal notation is now equal to 235

Final Answer