Page 58 - Computer Science V2.0 Class 11

(0.1) = (0.063146314…) = (0.06314) 8
10
8
↓
Recurring digits
The digits in bold are recurring digits. We truncate the recurring digits as per the requirement of accuracy.

Find decimal representation of (0.11) , (0.101) and (0.111) .
2
2
2

Decimal Numbers having Integer Part and Fraction Part To Octal number
To convert decimal numbers that have both an integer (whole number) and fractional part, the steps are as follows:
1. Convert the integer part to an equivalent octal number (say, a)
2. Convert the fraction part between 0 and 1 to an equivalent octal number between 0 and 1 (say, b).
3. Put the octal representation of the integer part and the fraction part adjacent to each other.
Example 26: Convert (902.7421875) to its octal equivalent.
10
8 902 Remainder
8 112 6
8 14 0
= (1606)
8 1 6 8
8 0 1

Fraction part Integer part
0.7421875 × 8 = 5.9375 0.9375 5
0.9375 × 8 = 7.5 0.5 7
0.5 × 8 = 4.0 0.0 4
(0.7421875) = (0.574) 8
10
So, (902.7421875) = (1606.574) 8
10
Example 27: Convert (902.82) to its octal equivalent, accurate to three places after the radix point.
10
8 902 Remainder

8 112 6
8 14 0
= (1606)
8 1 6 8
8 0 1

Fraction part Integer part
0.82 × 8 = 6.56 0.56 6
0.56 × 8 = 4.48 0.48 4 =(.643) 8
0.48 × 8 = 3.84 0.84 3
(902.82) = (1606.643) 8
10

Find octal representation of (3.25) , (20.50) and (32.125) .
10 10 10

44 Touchpad Computer Science (Ver. 2.0)-XI