Division of Decimal Fractions

The only difference between the division of whole numbers and that of numbers containing decimal fractions is that we must take into consideration the fact that some portion of either the dividend or the divisor or of both is fractional, as is indicated by the decimal point.

Furthermore, when we perform division with whole numbers, we often cannot complete this operation as we obtain a remainder. Thus, we have before us two questions:

1. Where shall we locate the decimal point in the quotient?

2. What shall we do in the case of a remainder?

We have examined the effect of moving of the decimal point. Let’s first examine the division of a decimal fraction by a whole number. For example 111.78 : 9. We shall proceed as in the division of whole numbers:

111.78 I 9

- 9 12

- 18

Note that the division of the whole part leaves a remainder 3, and that we have a fractional part 0.78. That is we are left with 3.78. From this point on we can't expect anything else but some fraction in the quotient if we continue the division. If now we bring down the next digit, that is 7, we shall have 3,7 or 370 tenths. If we divide 37 tenths by 9, we shall have a certain number of tenths in the quotient. We shall, therefore, place a decimal point after the 2 in the obtained

quotient and continue the division as usual. Then we shall have:

111.78 I 9 Check: I2.42

-9 12.42 x 9

21 111.78

-18

-36

-18

Thus we observe that division of a decimal fraction by a whole number is performed in the same manner as division of a whole number by a whole number.

The whole part of the decimal fraction will give the whole part of the quotient. As soon as we bring down the first digit from the decimal part of the dividend, we shall begin to obtain the decimal part (the fractional part) of the quotient. This procedure always serves for the division of decimal numbers by whole numbers.

Now we shall apply the results just obtained to the division of decimal fractions by decimal fractions. Let’s perform the division 176.28 : 2.6. We know that the multiplication of the dividend and of the divisor by the same number does not produce any change in the quotient. When we multiply the dividend by some number, the quotient is multiplied by the same number, but when we multiply the divisor by some number, the quotient is divided by the same number. This fact enables us to change the dividend 2.6 into a whole number. This change is accomplished by moving both decimal points one place to the right; thus, both the divisor and the dividend 176.28 and 2.6 are multiplied by 10. The divisor 2.6 becomes 26, and the dividend 176.28 becomes 1,762.8.

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