Several methods of determining decimal point location are discussed below. It is assumed you are already familiar with integer long division and can continue it to as many decimal places as required. (You can do 9/8 = 1.125, for example.) Express each as an integer divided by a power of 10. Compute the value of the fraction in the usual way. Example 12.34/2.683 = (1234/100)/(2683/1000) = 1234/2683*1000/100 = 12340/2683 (perform this division to get your answer) = 4.5993... Note that this is equivalent to adding enough zeros to the right of the shorter decimal so the numbers have the same number of digits to the right of the decimal point. Then remove the decimal points and treat the numbers as integers. 12.34 becomes 12.340 so it has 3 decimal fraction digits like 2.683 does. Now we treat the problem as 12340/2683 _____ It can also be convenient to use powers of 10 to rewrite the numbers to the form x.xxx...*10^yy then you only have to know whether the quotient is larger or smaller than 1. In the above example, this would look like (1.234*10)/(2.683) The quotient of 1.234/2.683 is smaller than 1 (because the denominator is larger), so the result will be .45993...*10 = 4.5993... The result of the division performed on these 1-digit numbers will always be between .1000...
and 9.999... Those of us who learned multiplication and division using a slide rule made much use of this method.
You can also pay attention to the "multiply the divisor by the quotient digit" part of the operation. This will tell you how big the multiplier has to be to make the product line up for subtraction. Example .0073/12 We know that 72/12 = 6. In order to have the correct product to subtract from .0073, we realize the multiplier must be .0006. Successive quotient digits will go to the right of that. Once the decimal position is determined, division proceeds as with integers.
and 9.999... Those of us who learned multiplication and division using a slide rule made much use of this method.
You can also pay attention to the "multiply the divisor by the quotient digit" part of the operation. This will tell you how big the multiplier has to be to make the product line up for subtraction. Example .0073/12 We know that 72/12 = 6. In order to have the correct product to subtract from .0073, we realize the multiplier must be .0006. Successive quotient digits will go to the right of that. Once the decimal position is determined, division proceeds as with integers.
