What is #24.73 -: 9#?

1 Answer
Apr 18, 2016

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

Explanation:

Long divide...

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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)#