Exercises: multiplying decimal numbers

Division of decimal fractions

$8.45:100$

Since $100$ is a multiple of ten, you can simply shift the decimal mark two places (one for each zero) to the left.

$8.45:100=0.0845$

Division of decimal fractions

$16:0.25$

Multiply both figures with $100$ to turn $0.25$ into an integer.

$\begin{array}{l}16:0.25\\ =(16\cdot 100):(0.25\cdot 100)\\ =1600:25\end{array}$

Utilize long division.

$\begin{array}{l}\phantom{25)}\underline{\phantom{.16}64}\\ 25)\phantom{-}1600\\ \phantom{25)}\underline{-150}\\ \phantom{25)}\phantom{-1}100\\ \phantom{25)}\phantom{0}\underline{-100}\\ \phantom{25)}\phantom{-000}0\end{array}$

$\Rightarrow 16:0.25=64$

Division of decimal fractions

$8.5:0.160$

Write the denominator as $0.16$ instead of $0.160$. Omitting zeros at the end of a decimal fraction does not change the figure.

$8.5:0.160=8.5:0.16$

Multiply both figures with $100$ to turn $0.16$ into an integer.

$\begin{array}{l}8.5:0.16\\ =(8.5\cdot 100):(0.16\cdot 100)\\ =850:16\end{array}$

Utilize long division.

$\begin{array}{l}\phantom{25)}\underline{\phantom{60}53.125}\\ 16)\phantom{-}850.000\\ \phantom{16)}\underline{-80}\\ \phantom{16)}\phantom{-1}50\\ \phantom{16)}\phantom{0}\underline{-48}\\ \phantom{16)}\phantom{-00}2.0\\ \phantom{16)}\phantom{00}\underline{-1.6}\\ \phantom{16)}\phantom{-00.0}40\\ \phantom{16)}\phantom{0.00}\underline{-32}\\ \phantom{16)}\phantom{-0.000}80\\ \phantom{16)}\phantom{000.0}\underline{-80}\\ \phantom{16)}\phantom{-000.00}0\end{array}$

$\Rightarrow 8.5:0.160=53.125$

Division of decimal fractions

$0.125:0.5$

Multiply both figures with $1000$ to turn $0.125$ into an integer.

$\begin{array}{l}\phantom{=.}0.125:0.5\\ =(0.125\cdot 1000):(0.5\cdot 1000)\\ =125:500\end{array}$

Utilize long division.

$\begin{array}{l}\phantom{251)}\underline{\phantom{160}0.25}\\ 500)\phantom{-}125.00\\ \phantom{500)}\underline{-\phantom{12}0}\\ \phantom{500)}\phantom{-}125.0\\ \phantom{500)}\underline{-100.0}\\ \phantom{500)}\phantom{-0}25.00\\ \phantom{500)}\phantom{0}\underline{-25.00}\\ \phantom{500)}\phantom{-000.0}0\end{array}$

$\Rightarrow 0.125:0.5=0.25$

Division of decimal fractions

$8.45:0.01$

Dividing a decimal fraction by $0.01$ shifts the decimal mark two places (one for each zero) to the right.

$8.45:0.01=845$