Decimal significand
= Decimal significand
{title2=$S_{10}(x)=10^{\{\log_{10}x\}}$}
For $x>0$, the <decimal significand> is the unique $S_{10}(x)\in[1,10)$ such that $x=10^kS_{10}(x)$ for an <integer> $k$. Explicitly, $k=\lfloor\log_{10}x\rfloor$ and $S_{10}(x)=10^{\{\log_{10}x\}}$, using the <floor function> and the <fractional part>. For $0.0042$, $4.2$ and $4200$, the <decimal significand> is $4.2$ and the first nonzero digit is $\lfloor S_{10}(x)\rfloor=4$. In the classical terminology of <logarithm> tables, the logarithmic mantissa is $\{\log_{10}x\}$, which differs from the <decimal significand> $10^{\{\log_{10}x\}}$.