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5
In this form, the decimals have a common denominator of 10 =100000:
10200 9876 20000
0.102 = 0.09876 = 0.2 = .
100000 100000 100000
Now, it is easy to see which has the largest numerator, which the second-largest, and which the smallest.
Hence we have
0.2 > 0.102 > 0.09876.

4.3.1 Exercises

Eliminate the insignificant 0’s in the following decimals.

1. 210304.0900

2. 00206.006070

3. 210.00
4. 21030900

Arrange each group of decimals in descending order, from largest to smallest:

5. 0.2, .009, .121.

6. 1.31, 1.9, 1.224.

7. 0.106, 0.5, 0.61.

8. 9.104, 9.14, 9.137, 9.099.

4.4 Rounding-off

The numbers
0.1, 0.11, 0.111, 0.1111, 0.11111

get closer and closer together (on the number line) as we move from left to right. After a few steps,
they are almost too close together to visualize. The second number was obtained from the first by
adding 1 , and the last from the second-to-last by adding just 1 , a very small quantity indeed.
100 100000
Such small quantities can be important in the sciences, but even in circumstances where precision is
important, there is always a limit beyond which small differences become negligible – not worth worrying
about. (For example, when your bank calculates the interest onyour savings account, it calculates, but
then ignores, amounts that are less than one half of one cent.) Being precise, but not overly precise, is
the purpose of rounding-off numbers.
To round off a number, we must first decide how precise to be. That means choosing the place
whose value we consider the smallest worth worrying about. For example, in negotiating an annual
salary, we would probably not argue about amounts less than $100, but in negotiating an hourly wage,
we would be willing to argue about pennies. In the first instance, we would round off our dollar amounts
to the nearest hundred, and in the second, to the nearest hundredth(cent).

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