Division with decimals

Division with decimals

We restrict our attention to cases where the quotient is a terminating decimal.

Division of decimals by whole numbers

If we had a piece of rope that was 4.8 metres long and wanted to cut it into 4 equal pieces we could cut it in 2 and then cut each piece in 2 again to get 4 pieces, each 1.2 metres in length. We can use the division algorithm to show this.

The procedure is the same as for whole numbers. The decimal point in the answer is aligned directly above the decimal point in the question.

We can relate this to division by fractions (invert and multiply).

	4.8 ÷ 4	= \(\dfrac{48}{10}\) ÷ \(\dfrac{4}{1}\)
		=\(\dfrac{48\hspace{-2.2mm}/^{12}}{10}\) × \(\dfrac{1}{4\hspace{-2mm}/\,^{1}}\)
		= \(\dfrac{12}{10}\)
		= 1.2.

If we were to divide a 4.8 metre piece of rope into 5 equal pieces, the procedure is a little more involved. We could divide 4.8 by 10 and double the result to get 0.96. This can be also be found using the division algorithm:

So, 4.8 cut into 5 equal lengths is 0.96. Each piece of the rope will be 0.96 metres 
in length.

Division of decimals by decimals