Math Problem Solver

\[ 0.106 - 0.0315=0.0745=\frac{149}{2000} \]

\[ \begin{aligned} &\mathtt{.}\overset{{\scriptscriptstyle \mathtt{0}}}{\cancel{\mathtt{1}}}\overset{{\scriptscriptstyle \mathtt{10}}}{\cancel{\mathtt{0}}}\overset{{\scriptscriptstyle \mathtt{5}}}{\cancel{\mathtt{6}}}\overset{{\scriptscriptstyle \mathtt{10}}}{\cancel{\mathtt{0}}}\\ \mathtt{-\phantom{0}}&\mathtt{.}\mathtt{0}\mathtt{3}\mathtt{1}\mathtt{5}\\ \hline &\mathtt{.}\mathtt{0}\mathtt{7}\mathtt{4}\mathtt{5} \end{aligned} \]

Borrow \(10^{-3}\), resulting in \(5\) in the \(10^{-3}\) place, and \(10\) in the \(10^{-4}\) place.

\(5\) is the digit in the \(10^{-4}\) place. \(10 \times 10^{-4} - 5 \times 10^{-4} = 5 \times 10^{-4}\).

\(4\) is the digit in the \(10^{-3}\) place. \(5 \times 10^{-3} - 1 \times 10^{-3} = 4 \times 10^{-3}\).

Borrow \(10^{-1}\), resulting in \(0\) in the \(10^{-1}\) place, and \(10\) in the \(10^{-2}\) place.

\(7\) is the digit in the \(10^{-2}\) place. \(10 \times 10^{-2} - 3 \times 10^{-2} = 7 \times 10^{-2}\).

\(0\) is the digit in the \(10^{-1}\) place. \(0 \times 10^{-1} - 0 \times 10^{-1} = 0 \times 10^{-1}\).