# Division of Decimal Real Numbers (w/o calc)

I'm getting stuck with what should be something easy for me, have been unable to find a tutorial online.

How would I do calculations like:

35.7 / 4.4

or

15.8 / 1.9

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I'd convert to fractions, do the division, and then maybe convert back to decimal. For the second, you have $\dfrac{158/10}{19/10}=\dfrac{158}{19}=8.315\dots$, where the last one can be done through the usual division method... – J. M. Nov 16 '11 at 19:27
Just note that $\frac{35.7}{4.4} = \frac{35.7}{4.4} \times \frac{10}{10} = \frac{357}{44}$. Then just do the long division like usual. – JavaMan Nov 16 '11 at 19:28

## 2 Answers

The standard school approach is basically what JavaMan suggested in the comments: multiply each number by a power of $10$ sufficient to make the divisor an integer, and then do an ordinary long division. Equivalently, move the decimal point in the divisor far enough to the right to make it an integer, then move the decimal point in the divident (numerator) the same number of places to the right, and do an ordinary long division. As an example, to divide $2.3$ by $5.21$ first move the decimal point two places to the right in each, so that you’re dividing $230$ by $521$. To divide $2.379$ by $5.21$ you would again move the decimal point in each number two places to the right and then divide $237.9$ by $521$ by ordinary long division:

       .45662...
------------
521)237.90000000
208 4
-----
29 50
26 05
-----
3 450
3 126
-----
3240
3126
----
1140
1042
----
980


Etcetera.

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I usually find it easiest to get rid of the decimal point by multiplying the number by 10 as many times as there are digits after the decimal point, just make sure that whatever you multiply one number by, you multiply another by the SAME number. Why this works? if you have a fraction say ${1\over 2}={1\times2\over 2\times2}={2\over4}$ or say ${1\over 2}={1\times3\over2\times3}={3\over6}$ so if you treat each division as a fraction ${35.7\over4.4}= {35.7\times10\over4.4\times10}={357\over44}$ then proceed by dividing top by bottom as normal. Can you work out what the other one should be? For practice, you can try ${1.5\over 0.3},{0.75\over 0.15},{7.5\over0.05},{12\over0.06}, {57\over0.02}$ I hope that will give you plenty of practice. You can get back to me for the answers to those, I want you to try them first.

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