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Convert the octal number $0.4051$ into its equivalent decimal number.

1. $0.5100098$
2. $0.2096$
3. $0.52$
4. $0.4192$

enter the number: 0.40518 in Octal number system and want to translate it into Decimal.
To do this, at first translate it to decimal here so :

0.40518 = 0∙80+4∙8-1+0∙8-2+5∙8-3+1∙8-4 = 0+0.5+0+0.009765625+0.000244140625 = 0.51000976562510

0.5100098

enter the number: 0.40518 in Octal number system and want to translate it into Decimal.
To do this, at first translate it to decimal here so :

0.40518 = 0∙80+4∙8-1+0∙8-2+5∙8-3+1∙8-4 = 0+0.5+0+0.009765625+0.000244140625 = 0.51000976562510

### 1 comment

For converting any base(say $n$) to decimal, we need to multiply the digits with their weights. And weights are equal to $n$ to the power place of the digit in the number, with respect to the radix point.

So, for converting $(0.4051)_8$ to decimal, we need to multiply the digits with their respective weights.

i.e.

$(0.4051)_8$

$= 0 \times 8^0 + 4 \times 8^{-1}+ 0 \times 8^{-2} + 5 \times 8^{-3} + 1 \times 8^{-4}$

$= 0.510009765625$

$\approx 0.5100098$

Hence option (A)

$Given \ (0.4051)^{_{8}} \\ Decimal \ equivalent = 0*8^{0}+4*8^{-1}+0*8^{-2}+5*8^{-3}+1*8^{-4}\\ = 0.51000976 \cong 0.510098$

Hence option a) is correct