# What is 24.73 -: 9?

Apr 18, 2016

$24.73 \div 9 = 2.74777 \ldots = 2.74 \overline{7}$

#### Explanation:

Long divide... Write the dividend $24.73$ under the bar and the divisor $9$ to the left.

Choose the first digit of the quotient so that when multiplied by the divisor it gives a value as large as possible, but less than or equal to the dividend.

We choose the value $\textcolor{b l u e}{2}$ since $2 \cdot 9 = 18 \le 24$ (whereas $3 \cdot 9 = 27 > 24$).

Write the product $18$ under the dividend and subtract it to give a remainder ($6$). Bring down the next digit ($7$) of the dividend alongside it.

Choose the next digit of the quotient to give a product $\le 67$ when multiplied by the divisor. This next digit is $\textcolor{b l u e}{7}$, the first digit after the decimal point.

Write the product $63$ under the running remainder to give a new remainder and bring down the next digit of the dividend alongside it.

Carrying on in this fashion we get digits $\textcolor{b l u e}{4}$ and $\textcolor{b l u e}{7}$, before we run out of non-zero digits to bring down from the dividend and the running remainder starts repeating.

As a result, the quotient starts repeating too and we have a recurring tail of $\textcolor{b l u e}{7}$'s.

One way of writing a repeating pattern of digits is to put a bar over it.

So we can write:

$24.73 \div 9 = 2.74777 \ldots = 2.74 \overline{7}$