Page 126 - ArithBook5thEd ~ BCC

As before, add the digits in each column starting from the right-most one, carrying when necessary:

98. 80
+3 4 2 . 0 3

44 0. 83
The sum is 440.83.

Example 155. Find the sum of 804.09, 56.384, 107, and 0.205.

Solution. Line up the numbers vertically at the decimal points (equivalently, at the ones place). In the
whole number 107, the decimal point is understood to be directly to the right of the ones place. Add
the columns from right to left, imagining 0’s in the empty places, and carrying when necessary.

80 4. 09
56 . 3 8 4
10 7.
+ 0 . 2 0 5

96 7. 6 79

Subtraction follows the same vertical alignment rule.
Example 156. Find the difference 50 − 4.706.

Solution. The larger number, 50, goes on top. We fill it out with insignificant 0’s so that both the
minuend and the subtrahend have the same number of decimal places.

50 . 00 0
− 4. 7 06

.
Borrowing from the tens place of the subtrahend, we can write

50.000 = 5 tens +0 ones +0 tenths +etc.
=4 tens +9 ones +9 tenths +9 hundredths + {10} thousandths

=49.99{10}

Then our subtraction becomes
49 . 9 9 {10}
− 4. 70 6

45 . 2 9 4

If we encounter negative decimal fractions, the usual sign rules apply (see Section 3.12).
Example 157. Find the sum −3.6 + 4.9.

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