Exercises

Calculate the solution of the following divisions:

$8.45:100$

### 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.

$8.45 :100=0.0845$

$16:0.25$

### Division of decimal fractions

$16:0.25$

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

$16:0.25\\=(16\cdot100):(0.25\cdot100)\\=1600:25$

Utilize long division.

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

$\Rightarrow16:0.25=\color{green}{64}$

$8.5 : 0.160$

### 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.

$8.5:0.16\\ =(8.5\cdot100):(0.16\cdot100)\\ =850:16$

Utilize long division.

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

$\Rightarrow8.5:0.160=\color{green}{53.125}$

$0.125:0.5$

### Division of decimal fractions

$0.125:0.5$

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

$\hphantom{=.}0.125:0.5\\=(0.125\cdot1000):(0.5\cdot1000)\\=125:500$

Utilize long division.

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

$\Rightarrow0.125:0.5=\color{green}{0.25}$

$8.45 : 0.01$

### 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.

$8.45:0.01=845$