# Express KB in bits

Express 126KB in bits, rounded to three significant figures?

I think i'm on the right track but honestly, I have no idea!

1KB = 2^10 (1024)
1024 = 1 Byte

1024 x 8 = 8192 (number of bits in byte)
8192 x 126 KB = 1032192 bits


I think it's right but different websites use different formulas.

• All you missed was the rounded part, the rounded answer would be $$103 \cdot 10^{4} = 1030000$$ – AlexR Nov 12 '14 at 18:53
• It would be better to put Bytes on the first line. Then 1024=1 Byte is wrong, and that line should just deleted. The next line should say 1024 Bytes/K x 8 bits/Byte=8192 bits/KB, then finally 8192 bits/KB x 126 KB=1032192 bits and your units and work are clear. Finally round to three places and you are done. – Ross Millikan Nov 12 '14 at 19:02

Note that you've written it down a bit sloppy, but your numbers are okay. \begin{align*} 1\ KB & = 2^{10}\ B = 1024\ B\\ 1\ B & = 8\ b \\ \Rightarrow 1\ KB & = 1024 \cdot 8\ b = 8192\ b \\ \Rightarrow 126\ KB & = 8192 \cdot 126\ b = 1032192\ b \approx 1030000\ b \end{align*} Three siginificant figures means the three digits starting with the first non-zero one, that is $103****$. Now fill the ignored digits with zeros to obtain the desired result.
Note that actually $1\ KB = 1000\ B$ (SI-prefix "kilo") and $1\ KiB =1024\ B$ (SI-prefix "kibi") but the definitions are inconsistent across different sites. Windows uses the $KiB$ but displays $KB$, for example.