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Convert 142 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 >= 142

8⁰ = 1

8¹ = 8

8² = 64

8³ = 512 <--- Stop: This is greater than 142

Since 512 is greater than 142, 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 142 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 <= 142, 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 142 is 1

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

Add our new value to our running total, we get:
128 + 8 = 136

This is <= 142, so we assign our outside coefficient of 1 for this digit.

Our new sum becomes 136

Our octal notation is now equal to 21

8⁰ = 1

The highest coefficient less than 7 we can multiply this by to stay under 142 is 6

Multiplying this coefficient by our original value, we get: 6 * 1 = 6

Add our new value to our running total, we get:
136 + 6 = 142

This = 142, so we assign our outside coefficient of 6 for this digit.

Our new sum becomes 142

Our octal notation is now equal to 216

Final Answer