Lesson 6
The Octal System
From eight to ten
Page 209
You are correct. An octal fraction such as
.7628 can be converted to a decimal fraction by writing the number in expanded form, as shown below. (We always write the expanded form of a number with
decimal numerals, for no particular reason other than the fact that decimal numerals are familiar and therefore convenient to work with.)
.7628
= 7( 8 − 1 ) + 6( 8 − 2 ) + 2( 8 − 3 )
= 7⎛ ⎝ ( 1 )/( 81 ) ⎞ ⎠ ⎛ ⎝ ( 1 )/( 82 ) ⎞ ⎠ ⎛ ⎝ ( 1 )/( 83 ) ⎞ ⎠
= 7⎛ ⎝ ( 1 )/( 8 ) ⎞ ⎠ ⎛ ⎝ ( 1 )/( 64 ) ⎞ ⎠ ⎛ ⎝ ( 1 )/( 512 ) ⎞ ⎠
Now, as you can see, the arithmetic is going to get a little sticky here:
( 1 )/( 8 ) 10 ; ( 1 )/( 64 ) 10 ; ( 1 )/( 512 ) 10 .
Our sum is actually .9726562510 = .7628 .
Now it’s your turn. Convert .548 to a decimal fraction by expansion.
Answer to Self-Test Question 5, Lesson 6 :
a . ( 1 )/( 8 ) b . ( 1 )/( 64 ) c . ( 1 )/( 512 )
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