Convert the decimal number 18.625_{10} to a number in base 8. What is the equivalent value… — JAMB UTME

Convert the decimal number $18.625_{10}$ to a number in base 8. What is the equivalent value in base 8?

The equivalent value in base 8 is

22.5_8

Converting the whole number part

18_{10}

to base 8 gives

22_8

because

18 = 2 \times 8^1 + 2 \times 8^0

. Converting the fractional part

0.625_{10}

to base 8 involves multiplying by 8:

0.625 \times 8 = 5.0

, giving

.5_8

. Thus,

18.625_{10} = 22.5_8

Convert the integer part (

18

) from base 10 to base 8.

18 \div 8 = 2

with a remainder of

2

. Reading the digits upwards gives

22_8

Successive division by 8 extracts the octal place values for the whole number.

Convert the fractional part (

0.625

) from base 10 to base 8.

0.625 \times 8 = 5.0

. The whole number part of the product is

5

, so

0.625_{10} = 0.5_8

Successive multiplication of the fractional part by the target base isolates the negative powers of the base.

Combine the converted integer and fractional parts.

22_8 + 0.5_8 = 22.5_8

The full representation is the sum of the integer and fractional base 8 components.

Fractional Base Conversion

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