Question

What is `24.73 -: 9`?

Answer 1

`24.73-:9 = 2.74777... = 2.74bar(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 `color(blue)(2)` since `2*9 = 18 <= 24` (whereas `3*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 `<=67` when multiplied by the divisor. This next digit is `color(blue)(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 `color(blue)(4)` and `color(blue)(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 `color(blue)(7)`'s.

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

So we can write:

`24.73 -: 9 = 2.74777... = 2.74bar(7)`