Answer :
Final answer:
The decimal number 528.625 can be represented as:
- Binary: 1000010000.101
- Octal: 1020.5
- Hexadecimal: 210.A
Explanation:
To convert the decimal number 528.625 to different number systems:
- Binary: Divide 528 by 2 and record the remainders: 528 ÷ 2 = 264 remainder 0. Repeat this process with the quotient until the quotient becomes 0. The remainders, read from bottom to top, give us the binary representation: 1000010000. For the fractional part, multiply 0.625 by 2 and record the whole number part: 0.625 × 2 = 1.25, so the fractional part becomes 1. Repeat this process with the fractional part until the fractional part becomes 0 or until the desired precision is achieved. The binary representation of the fractional part is 0.101. Therefore, the binary representation of 528.625 is 1000010000.101.
- Octal: Divide 528 by 8 and record the remainders: 528 ÷ 8 = 66 remainder 0. Repeat this process with the quotient until the quotient becomes 0. The remainders, read from bottom to top, give us the octal representation: 1020. For the fractional part, multiply 0.625 by 8 and record the whole number part: 0.625 × 8 = 5, so the fractional part becomes 5. Repeat this process with the fractional part until the fractional part becomes 0 or until the desired precision is achieved. The octal representation of the fractional part is 0.5. Therefore, the octal representation of 528.625 is 1020.5.
- Hexadecimal: Divide 528 by 16 and record the remainders: 528 ÷ 16 = 33 remainder 0. Repeat this process with the quotient until the quotient becomes 0. The remainders, read from bottom to top, give us the hexadecimal representation: 210. For the fractional part, multiply 0.625 by 16 and record the whole number part: 0.625 × 16 = 10, so the fractional part becomes A. Repeat this process with the fractional part until the fractional part becomes 0 or until the desired precision is achieved. The hexadecimal representation of the fractional part is A. Therefore, the hexadecimal representation of 528.625 is 210.A.
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