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Answer
Success!
We are done. 248 converted from decimal to octal notation equals 3708.

↓Steps Explained:↓

Convert 248 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 >= 248

80 = 1

81 = 8

82 = 64

83 = 512 <--- Stop: This is greater than 248

Since 512 is greater than 248, 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 248 is 3

Multiplying this coefficient by our original value, we get: 3 * 64 = 192

Add our new value to our running total, we get:
0 + 192 = 192

This is <= 248, so we assign our outside coefficient of 3 for this digit.

Our new sum becomes 192

Our octal notation is now equal to 3


81 = 8

The highest coefficient less than 7 we can multiply this by to stay under 248 is 7

Multiplying this coefficient by our original value, we get: 7 * 8 = 56

Add our new value to our running total, we get:
192 + 56 = 248

This = 248, so we assign our outside coefficient of 7 for this digit.

Our new sum becomes 248

Our octal notation is now equal to 37


80 = 1

The highest coefficient less than 7 we can multiply this by to stay under 248 is 1

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

Add our new value to our running total, we get:
248 + 1 = 249

This is > 248, so we assign a 0 for this digit.

Our total sum remains the same at 248

Our octal notation is now equal to 370


Final Answer

We are done. 248 converted from decimal to octal notation equals 3708.
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