9514 1404 393
Answer:
0.0806451612903225806...
Step-by-step explanation:
It is much easier to keep place values straight in long division when the divisor is an integer. Consequently, the usual approach is to move the decimal point in the divisor until an integer is formed. Then the same movement of the decimal point is done to the dividend.
3.962 needs to have its decimal point moved 3 places to the right to make it be an integer. Effectively, we need to multiply the number by 1000.
When we multiply the dividend 0.32 by 1000, it becomes 320. So, the division problem is essentially rewritten to ...
0.32/3.968 = 320/3968
Long division proceeds in the usual way. The quotient digit is multiplied by the divisor and that result is subtracted from the dividend to get the new dividend. The steps are shown in the attachment.
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The fraction shown above can be further reduced so the problem is equivalent to 5/62. The decimal fraction has a 15-digit repeat. (You can't see that with the work shown in the attachment. Additional steps can show this. So can a suitable calculator.) You can tell when the quotient will repeat, because the dividend value will be one you have seen before.
