8.4 Decimals: division of decimals  (Page 2/3)

$\text{32}\text{.}\text{66}÷7\text{.}1$

$7.1\overline{)32.66}$

• The divisor has one decimal place.
• Move the decimal point of both the divisor and the dividend 1 place to the right.
• Set the decimal point.
• Divide as usual.

Thus, $\text{32}\text{.}\text{66}÷7\text{.}1=4\text{.}6$ .

Check: $\text{32}\text{.}\text{66}÷7\text{.}1=4\text{.}6$ if $4\text{.}6\times 7\text{.}1=\text{32}\text{.}\text{66}$

$\begin{array}{cc}\hfill 4.6& \\ \hfill \underline{\times 7.1}& \\ \hfill 46& \\ \hfill \underline{322}& \\ \hfill 32.66& \text{True.}\hfill \end{array}$

$1\text{.}\text{0773}÷0\text{.}\text{513}$

• The divisor has 3 decimal places.
• Move the decimal point of both the divisor and the dividend 3 places to the right.
• Set the decimal place and divide.

Thus, $1\text{.}\text{0773}÷0\text{.}\text{513}=2\text{.}1$ .

Checking by multiplying 2.1 and 0.513 will convince us that we have obtained the correct result. (Try it.)

$\text{12}÷0\text{.}\text{00032}$

$0.00032\overline{)12.00000}$

• The divisor has 5 decimal places.
• Move the decimal point of both the divisor and the dividend 5 places to the right. We will need to add 5 zeros to 12.
• Set the decimal place and divide.

This is now the same as the division of whole numbers.

$\begin{array}{c}\hfill 37500.\\ \hfill 32\overline{)1200000.}\\ \hfill \underline{\mathrm{96 }}\\ \hfill \mathrm{240 }\\ \hfill \underline{\mathrm{224 }}\\ \hfill \mathrm{160 }\\ \hfill \underline{\mathrm{160 }}\\ \hfill 000\end{array}$

Checking assures us that $\text{12}÷0\text{.}\text{00032}=\text{37},\text{500}$ .

$\text{12}\text{.}\text{596}÷4\text{.}7$

Since the display is not filled, we expect this to be an accurate result.

$0\text{.}\text{5696376}÷0\text{.}\text{00123}$

Since the display is not filled, we expect this result to be accurate.