We discard the digits 2 and 3. But we do not simply ignore these discarded digits. They may cause a change in one of the digits we intend to use. If we have 45.6723

+ 156.7

then according to the following rule we must rewrite it as:

45.7

+ 156.7

If the first digit at left of the portion that is to be discarded is either 0,1,2,3, or 4, then the last digit on the right that is to be retained should be left unchanged. If the first digit at the left of the portion that is to be discarded is either 5,6,7,8, or 9, then the last digit on the right that is to be retained should be increased by 1. Such discarding of the unnecessary decimal places is known as the rounding of numbers.

When 45.6723 was rounded to one decimal place, that is to tenths, we obtained 45.7 because the first digit of the discarded portion was 7, and therefore, the last digit on the right (the 6) was increased by 1, and we thus obtained 7. The actual addition and subtraction of decimal fractions are performed in the same manner as in the case of the whole numbers so that decimal points are all in a vertical column as is shown below: 56.883 or 875.728

+123.784 - 648.917

25.075 226.811

205.742

Multiplication of Decimal Fractions

The only difference between multiplication of whole numbers and decimal fractions is that we must take into consideration that some portion of one or both factors is fractional, as indicated by the decimal points. Now, instead of multiplying decimal fractions let us multiply whole numbers 3,672 and 275. To obtain 3,672 from 3.672 we move the decimal point 3 places to the right, that is we multiply the number by 1,000 and to obtain 275 from 2.75 we move the decimal point two places to the right. That is we multiply it by 100. Thus, the product 3,672 x 275 is 1000 x 100 = 100,000 times the product 3.672 x 2.75. When the product of the whole numbers 3,672 x 275 is obtained, we must divide it by 100,000. That is, we move the decimal point 5 places to the left. The multiplication of the whole number looks as follows:

3.672

x 275

+ 25704

7344

The decimal point (not written) is at present on the extreme right of the product, that is, we have 1,009,800 and after moving it 5 places to the left we have 10,098.

Notice that one factor has 3 decimal places, and the second factor has 2 decimal places. The product has 5 decimal places. That is the number of the decimal places in the product is equal to total number of decimal places in the factors.