convert the octal number to decimal  ---  0.5675 (8)

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txmedteach | High School Teacher | (Level 3) Associate Educator

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This question seems daunting initially, but decimals in octal work a lot like decimals in base 10. For us, if we see 0.5675 in decimal, we can also express it as:

`5/10+6/100+7/1000+5/10000 = 5*10^-1 + 6*10^-2 + 7*10^-3 +5*10^-4`

The same principle is behind the decimal in octal. The above octal number can be expressed as:

`5*8^-1 + 6*8^-2 + 7*8^-3 + 5*8^-4`

In other words:

`5/8 + 6/64 + 7/512 + 5/4096`

Now, few people can convert this easily to a decimal without some massive long division, so let's just use a calculator to add these fractions to get our resultant base-10 decimal (redundant, I know):

`5/8+6/64+7/512+5/4096 = 0.733642578125`

And you're done!

Side Note: It's a long decimal, but you'd expect that because for every power of `1/2` you end up adding a digit to the length of your decimal in its fully-reduced form. For example: `1/2 = 0.5` , `1/4 = (1/2)^2 = 0.25` , etc. Our largest denominator is 4096, making the fraction a multiple of `(1/2)^12` so, we should expect our decimal to have 12 digits, no more, no less (which it does!).

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