Given below are two statements with reference to number systems. In the light of the above statements, choose the most appropriate answer from the options given below.
Statement I:(0.5625) in base 10 equals (0.9) in base 16.
Statement II:(0.3) in base 10 equals (0.4BBB...) in base 16.
ABoth Statement I and Statement II are correct
BBoth Statement I and Statement II are incorrect
CStatement I is correct but Statement II is incorrect ✓ Correct
DStatement I is incorrect but Statement II is correct
Correct answer: (C) Statement I is correct but Statement II is incorrect
Explanation
Statement 1 is correct because 0.9 in hexadecimal is nine sixteenths, which equals 0.5625 in decimal.
Statement 2 is incorrect since 0.3 in decimal converts to 0.4CCC repeating in hexadecimal, not 0.4BBB.
Multiplying 0.3 by sixteen gives 4.8, so the first hex digit is 4 and the remainder continues.
The repeating digit works out to C, the hex value for twelve, not B.
A fraction converts to hexadecimal by repeated multiplication by sixteen.
Many simple decimals become non terminating fractions in other bases.
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