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I feel this question has too many questions inside it, I have since made a question that just asks a single division problem called Decimals: Division (includes rounding the answer).

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Dividing with decimals is a bit messy so we generally rewrite the division in an equivalent way by moving the decimal place in both numbers the same number of places.

For example, given the division $0.12 \\div 1.034$, we can see the second decimal has the most decimal places and we would need to move the decimal point three places to make it a whole number. So we move the decimal point in both decimals three places and rewrite the question as $120\\div 1034$.

Note: Moving the decimal place three times is really the same as multiplying by $10^3$.

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When asked to divide decimals $\\var{num1/1000} \\div \\var{num2/100}$ it is standard practice to evaluate the equivalent whole number division [[0]] $\\div$ [[1]] to make the calculation easier.

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Rewrite your division question in terms of whole numbers and then use long division to determine the answer. Instead of writing down a remainder at the end continue the long division process by adding zeroes (as many as you need) and using as many decimal places as you need.

Evaluate the following:

$\\var{dec1}\\div\\var{int1}=$[[0]]

$\\var{int2}\\div\\var{dec2}=$[[1]]

$\\var{termnum1}\\div\\var{termden1}$=[[2]]

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Do the same as the previous questions except you will continue until you start getting digits in your answer that you have seen already (since this will tell you what your repeating digits are) or you get to the seventh decimal place (so you can round to the sixth decimal place).

For example, say you are doing a division and you are building up your answer one digit at a time using long division, suppose you have 1.2749 so far and then you get another 7. Last time you got a 7 it resulted in the next number being a 4, then a 9 and then a 7 again. Hopefully you can see that the digits 749 will repeat and the answer will be 1.2749749749749749... Since we asked for six decimal places you look at the seventh decimal place to decide how to round, in this example your final answer would be 1.274975

Note, sometimes the length of the block of repeating digits is quite long and so you will not see it repeat until after the sixth decimal place. In this case (since the question asked to round to six decimal place) evaluate the answer to seven decimal places and then round to six decimal places.

The following should result in a repeating/recurring decimal, that is, there will be a repeating pattern of numbers. Write your answer rounded to 6 decimal places.

$\\var{renum}\\div \\var{reden}=$[[0]]

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[ 2, 4, 8, 10, 16, 20, 32, 40, 50, 80, 100, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000 ]

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