When I do Math.ceil(510/11*11) on Google Chrome, I get an answer 511 whereas if I do Math.ceil(510) or Math.ceil(510.00), I get the correct answer of 510. May I know why is it calculated like this? Apparently I tried some other numbers like 410, 610, etc.. and they were calculated correctly. Is there some documentation somewhere that someone can direct me to learn more about this?
Consider the following code:   0.1 + 0.2 == 0.3  -&gt;  false   0.1 + 0.2         -&gt;  0.30000000000000004   Why do these inaccuracies happen?
My windows directory is huge I know that the harmonic series $$\sum_{k=1}^{\infty}\frac{1}{k}  = \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \cdots + \frac{1}{n} + \cdots \tag{I}$$ diverges, but what about the alternating harmonic series   $$\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k}  = \frac{1}{1} - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} - \frac{1}{6} + \cdots + \frac{(-1)^{n+1}}{n} + \cdots \text{?} \tag{II}$$  Does it converge?   If so, what is its sum? How to resolve BackgroundContainer.dll error on startup? When I start my desktop it gives me an error about BackgroundContainer.dll.    How to get rid of it?  I found nothing when i started regedit.exe and searched (F3 or CTRL+F) for BackgroundContainer.dll Can I install any iOS version I wish by picking and choosing which firmware to restore? I'm trying to downgrade my iPhone from the current iOS to an older one, as per .  But every time I try, I always receive this error:     The iPhone could not be restored. This device isn't eligible for the requested build.     I have tried many times with and without DFU mode. Any ideas regarding this? On  (but I remember seeing it in other cases) the diff shows the same tag being both added and removed. Why is observing 100 heads for a fair coin flips surprising? Assume that we have a fair coin. We flip it 100 times. The outcome is all heads. Why is it surprising? Doesn't all outcomes have the same probability? Any particular outcome, including irregular ones, would have the same very small probability. Why is it that observing an irregular outcome is less surprising to us than a regular one? Pretty self descriptive, without being able to view the source of the noise how can we tell the difference between a sound in front of us and a sound behind us if pitch, volume and distance are all the same.   Also assume that it is not biased to one side more than the other, e.g its not to your left or right but directly in front or behind.   I'm interested in knowing if it is a part of the ear that makes this distinction, or a function of the brain. Trying to identify a very old short story about aliens colonizing human bodies Don't remember the exact start to the story, but it went something like "walking along a path" or something, and when he hears what sounds like a shotgun blast behind him, he then feels something strike him in the butt. He passes out, and when he awakens, he discovers that the "shotgun blast" was actually a miniature spaceship that exploded and shot miniature aliens into his body. The aliens prove to be very beneficial because they clean up all the toxins and other poisons in his body. They can be transmitted through kissing or sexual activity.  Any help with the name of the story would be greatly appreciated.  Dan The new top bar layout is fine, but the black color is very visually jarring/intrusive.  Is using a lighter color an available option? siunitx tabular numbers with separated uncertainty I would like to format the space reserved for a number shown in a table with separated uncertainty. It seems that when I use the table-format option the brackets around the mantissa disappear. This is illustrated in the example below:  \documentclass{article}     \usepackage{siunitx}  \begin{document}     \begin{table}   \begin{tabular}{                   S[separate-uncertainty = true]                   S[table-format=1.1(1)e1,                   separate-uncertainty = true]                   }     {Header} &amp; {Header}\\     1.0(2)e2 &amp; 1.0(2)e2\\   \end{tabular} \end{table}     \end{document}     I have also tried to use the bracket-numbers and multi-part-units = brackets without solving this issue. Is there any workaround to center the number and keep the brackets like in the first column of the example? How assign shortcut to custom function? How can I require a generic parameter to be an enum that implements an interface? Getting Session ID in Lightning I am aware that the "Eye of Sauron" in Peter Jackson's movies was not Sauron's actual physical form.  What the answers at '' don't indicate is, despite this, what abilities of vision Sauron may have had.  Did he have the ability to see from afar? If so, what are his limitations or details of this power? Is it some kind of Elvish-sight like Legolas but stronger? Was it a magical power? Or perhaps with the help of the Palantir (I'm not sure of this last one because I dont remember if the Palantir could only see what other Palantíri were seeing or anything he wanted)? Why would a company care about the price of its own shares in the stock market? How to properly typeset multiletter quantities, e.g. Re or Nu (Reynolds, Nusselt numbers) Is there a canonical way to typeset such quantities in equations and inline math?  \documentclass{article} \begin{document} $Re$, $Nu$ are clearly not an option. $\mathit{Re}$, $\mathit{Nu}$ appear ok to me. \end{document} Word for "the entire back part of the body"? When we lie down, the "back part of the body" is in contact with the bed. It includes the heels, the calves, the backside, the back, and the back of the neck, and the back of the head etc.  How do we refer to the entire "back part" of the body? Upon realizing it is a sarcophagus, he decides to sacrifice himself (I think by disconnecting his air) and exist in it for eternity along with the original creature. It may have been in an old Omni magazine, or some other periodical. I thought it may have been in the anthology "Dead Astronauts" but I did not find the story in there. Inbox notification and reputation score is misaligned in mobile web view The inbox notification indicator and reputation score indicator are misaligned in the mobile web view. What do you do when the bus bike rack is full? Sometimes I take commute via bike, other times on the bus, but I rarely plan on doing both because I worry about the possibility of waiting for a bus only to find that its bike rack is full and having to wait for the next bus, which may also have a full bike rack.  What do you do in this case? I asked a bus driver today on the way home and I couldn't really understand what he was saying, but he said something about a bike rack in the back and I think he was saying that were he not driving the rapid bus and were his schedule different, he would put any extra bikes in the back. Not sure though, he could have said something completely different.