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Subtraction of decimal numbers is done in a manner similar to addition in that the numbers are positioned with the decimal point lined up Also, as in the subtraction of ordinary numbers, the smaller decimal number must be subtracted from the larger decimal number For example, subtracting the number 6821 from 3749 can be done as below: 37490 6821 30669 Note that the zero added at the end of 37940 does not alter the value of the number and just serves as a placeholder in the subtraction operation
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You multiply two decimal numbers just as you would multiply two ordinary numbers In this case, however, the decimal points do not have to be lined up Knowing where to put the decimal point is important, but you can deal with it after you nish multiplying the two numbers For example, when the two decimal numbers 74 and 36 are multiplied, the two numbers are multiplied without regard to the decimal point, yielding a result of: 74 36 2664 To determine the placement of the decimal point in the product, you must rst determine the position of the decimal point in each of the two numbers being multiplied For the rst decimal number, because there is only one number following the decimal point, its fraction part is 1 The same can be said for the second number; its fraction part is also 10
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1 The combined fraction part of the product of these two numbers is 1 1 = 1 , 10 10 10 100 which is then multiplied by the result of the multiplication to yield the correct answer: 1 2664 = 2664 100 Yet another way of approaching this is to look at each decimal number and count the number of positions it takes to move from the decimal point to the end of the value For 74, it takes one position to move from the decimal point to the end of the number Similarly, for 36, it takes one position to move from the point to the end of the number For both numbers being multiplied, it takes a combined two positions moved from their decimal point Once the product is obtained, begin at the end of the number and move to the left the number of combined positions determined for each of the numbers being multiplied So, once the product of 2664 is obtained, you start to the right of 4 and move to the left two positions This is where the decimal point should be placed EXAMPLE: Find the product of 278 and 613 The product of these two decimal numbers can be found by rst multiplying the two numbers and ignoring the decimal point: 202 314 63428 Second, for each number being multiplied, the number of positions that you move from the decimal point to the end of the number must be determined For 202, one position is needed to move from the decimal point to the end For 314, two positions are needed Adding the number of positions results in a combined number of 3 Finally, returning to the product, you begin at the end of the number and move to the left three positions, or 202 314 63428
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Decimal numbers can be divided in the same way as ordinary numbers The position of the decimal point in the quotient can be determined when division is expressed in long division form Consider the following division problem: 48384 384 or 384 48384 , where 48384 is the dividend and 384 is the divisor If there were no decimal point in the divisor, then the decimal point in the quotient would be placed exactly above the dividend However, because there is a decimal point in the divisor, it is best to move it to the end of the number by multiplying the divisor by an appropriate factor The factor in this case is 10 because the single digit following the decimal
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