Exercise 4.1. Answer the following questions.

• What is a rational number ?

• Which fraction is called proper? Which fraction is called improper?
Give two examples of proper fractions and two examples of improper
fractions. Explain.

• Which number is called a mixed number? Give two examples of a
mixed number.

• What is a decimal number ? What is a terminating decimal number?
What is a repeating decimal number ?

Exercise 4.2. Reduce the following fraction to its lowest terms. Determine
whether this number is proper fraction or not . If not, present it as a mixed

Exercise 4.3. Present each decimal number as a ratio of two integers. DO
NOT reduce the fraction into lowest terms.

• 0.2345, 0.452 (terminating)

Solution .

Let We multiply this number by 10, 100,
1000, etc. until we see how to get rid of the repeating part.

We get

We see that 100a and a have the same
digits after the decimal point. Then,

Let Then,

We can see that the numbers 10a and 1000a have the same digits after the
point. Therefore,Thus,

Exercise 4.4. Evaluate the expression. Explain each step.

Exercise 4.5. To repair his sprinkler system, Tony Gambino needs a total
inches of PVC pipe. He has on hand pieces that measure 4 inches,
inches, and 1/4 inches in length. If he can combine these pieces and use them
in the repair, how long of piece of PVC pipe will Tony need to purchase to
repair his sprinkler system ?

Solution . First, we compute how much pipe is possessed by Tony Gambino.

So, he already has 638 inches of the pipe.

Second, we compute how much of the additional pipe he needs to buy.
We get
Therefore, he needs to buy additional inches of PVC pipe.

Exercise 4.6. What is the perfect square? Write down all perfect squares
less than 200.


Exercise 4.7. Evaluate

Solution. Fsing the results from Exercise 4.6, we get

Exercise 4.8. Simplify the radicalsand


Exercise 4.9. Perform the indicated operation. Simplify the answer when

Solution. First, we simplify all square roots:

Second, we gather all terms :

Exercise 4.10. Rationalize the denominator.

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