Question

the representation of octal number (532.2)8 in decimal is
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Answer 1

Answer:

The representation of octal number (532.2)8 in decimal is : O (346.25)10.

Answer 2

Answer:

The decimal representation of the octal number $(532.2)_{8}$ is $(346.25)_{10}$.

Octal Number System:

• A number system that has its base as eight is called an octal number system.
• The numbers in this number system are formed using the digits 0 to 7 only.
• For example, the numbers in the octal numbers are 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, and so on.

Explanation:

• To convert an octal number to a decimal number, we multiply each digit of the given octal number by the corresponding powers of eight and add them.
• The digit in the unit's place will be multiplied by the zeroth power of eight, the digit in the tens place will be multiplied by the first power of eight, the digit in the thousands place will be multiplied by the second power of eight, and so on.
• The digits after a decimal point in a given octal number are multiplied by the corresponding negative powers of eight.

Therefore,

$(532.2)_{8} = (5*8^{2}) + (3*8^{1})+(2*8^{0} )+(2*8^{-1} )$

$(532.2)_{8} = (5*64) + (3*8)+(2*1 )+(\frac{2}{8} )$

$(532.2)_{8} = 320+24+2+\frac{1}{4}$

$(532.2)_{8} = 346+0.25$

$(532.2)_{8} = (346.25)_{10}$

Therefore, the representation of the octal number $(532.2)_{8}$ in decimal is $(346.25)_{10}$.

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