The two statements given below are : Statement (I) : (0.5625) base 10 =…
2023
The two statements given below are :
Statement (I) : (0.5625) base 10 = (0.9)16
Statement (II) : (0.3) base 10 = (0.4BBB...)16
In the context of the above statements, choose the correct answer from the options given below :
- A.
Both Statement I and Statement II are true
- B.
Both Statement I and Statement II are false
- C.
Statement I is true, but Statement II is false
- D.
Statement I is false, but Statement II is true
Attempted by 41 students.
Show answer & explanation
Correct answer: C
To convert decimal to hexadecimal, multiply the fractional part by 16 repeatedly. For Statement I: 0.5625 × 16 = 9, giving digit 9. Thus, (0.5625)₁₀ = (0.9)₁₆ is true. For Statement II: 0.3 × 16 = 4.8 (digit 4), then 0.8 × 16 = 12.8 (digit C). The expansion is (0.4CCCC...)₁₆, making Statement II false.