Page 125 - ArithBook5thEd ~ BCC

One final remark about step 2 of the procedure. If the digit in the round-off place is 9, and we need
to round up (to 10), we must carry the 1 to the left-neighboring place.
Example 153. Round 6.597 to the nearest hundredth.

Solution. The 9 in the round-off place has right-neighbor 7, which is greater than 5. So we increase 9
to 10, and carry the 1 to the (left-neighboring) tenths place:

6.597 ≈ 6.60 (to the nearest hundredth)

Notice we preserved the insignificant 0, since it is in the round-off place.

4.4.1 Exercises

Round off each number twice: (a) to the nearest ten; (b) to the nearest hundredth.

1. 304.0900

2. 96.075
3. 115.497

4. 100.0055

5. 7.009

4.5 Adding and Subtracting Decimals

One of the advantages of decimals over ordinary fractions is ease of computation. The four operations
(addition, subtraction, multiplication and division) are done almost exactly as with whole numbers. The
only question is where to put the decimal point.
Addition and subtraction are the easiest: we line up the numbers vertically, with the ones places
aligned on top of eachother. This puts the decimal points in alignment as well. The decimal point in the
sum is placed directly below the decimal points in the numbers being added. Carrying and borrowing
are done as with whole numbers.

Example 154. Find the sum of 98.8 and 342.03.
Solution. Line up the numbers vertically so that the ones places (and hence the neighboring decimal
points) are directly on top of eachother.

98. 8
+3 4 2 . 0 3

For clarity, you can “pad out” the top number with an insignificant 0 so that both numbers have the
same number of decimal places. (This is not strictly necessary: just remember that an empty place is
occupied by a 0.) Place a decimal point, vertically aligned with the others, where the sum will go.

98. 80
+3 4 2 . 0 3

.

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