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Add $\bar4.74628$ and $ 3.42367$

This question is about characteristics and mantissa. I thought my book has written the wrong answer in the example. I just wish to cross check because this seem like something a kid would ask.

They do it like $-4+0.74628+3+0.42367=-1+1.16995$

But in the end the book writes $1-0.16995$. I thought it should be only $0.16995$

If I am doing it wrong or have not understood something could anyone please guide me.

JMP
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Ishan Taneja
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  • Your calculation is correct $-$ the answer is $0.16995$. – TonyK Apr 15 '16 at 11:34
  • Ok thanks,I got confused thinking this must be some property related to characteristics etc. – Ishan Taneja Apr 15 '16 at 11:35
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    What is $\bar4.74628$ and how is this question related to logarithms? – gammatester Apr 15 '16 at 11:40
  • @gammatester In my book they defined characteristics and mantissa in logarithms.$\bar4.74628$ is $-4$ and $+.74628$ – Ishan Taneja Apr 15 '16 at 11:41
  • @gammatester: You are showing your youth! In my day, we had to add logarithms by hand. To ease the drudgery, negative logarithms were written using the bar-notation: $\bar x.y = -x + 0.y$. For example, $\bar 4.3 = -3.7$. – TonyK Apr 15 '16 at 12:11
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    @TonyK: You are showing your youth! -- I also did this in high school (4th year "Advanced Math" = precalculus class, 1974-1975) but I don't recognize the overbar notation. But maybe I forgot, so I checked with my textbook, and this notation is not used there. Probably if I had access to a large library (and not a rural library with a 3 or 4 school algebra texts and 1 calculus text) I would have encountered it, but back then of course we didn't have the seemingly infinite resources of the internet. By the way, here's how we did these things. – Dave L. Renfro Apr 29 '23 at 13:26
  • Even if we defined $\bar 4.3$ to mean $-4 + .3$ (a seemingly bizarre definition), nobody has explained what this has to do with logarithms. – littleO Apr 30 '23 at 09:29
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    @littleO: nobody has explained what this has to do with logarithms -- The OP said "This question is about characteristics and mantissa." Recall these are the integer and positive decimal part of a logarithm's (decimal notation) value. For example, as approximations and using base-$10$ logs we have: (1) $\log 844 = 2 + 0.9263,$ so the characteristic is $2$ and the mantissa is $0.9263.$ (2) $\log 0.00345 = -2.4622 = -3 + 0.5378,$ so the characteristic is $-3$ and the mantissa is $0.5378.$ (continued) – Dave L. Renfro Apr 30 '23 at 12:50
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    The overbar notation for (2) is $\bar3.5378,$ the overbar (which I supposed can be interpreted as a raised negative sign) appearing only over the digit $3$ to signify that only the $3$ is negative. For those not familiar with numerical work using logarithm tables, see the MSE answer I previously cited to understand why one would consider characteristics and mantissas of a logarithm's value. – Dave L. Renfro Apr 30 '23 at 13:01
  • @DaveL.Renfro Thanks! I should’ve followed the link you gave earlier. – littleO Apr 30 '23 at 18:50

1 Answers1

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I had the same query! Here is how I understood it. Hope it helps:

In simple terms, logarithms have 3 types of notations

  1. 3.6622 = 3 + 0.6622

  2. -3.6622 = -3 - 0.6622

  3. 3¯.6622 = -3 + 0.6622

And it is to be noted that antilog can only be taken of positive mantissa. So you need to only be worried about the second case and rewrite it as -4 + 0.2278 for using it in antilog.

Pragati Bhattad
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