# MATH HOMEWORK 04

**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

number.

**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)

• (repeating)

** 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,

Therefore,

Let Then,

We can see that the numbers 10a and 1000a have the same digits after the

decimal 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.

**Solution**.

**Exercise 4.7**. Evaluate

**Solution.** Fsing the results from Exercise 4.6, we
get

**Exercise 4.8. **Simplify the radicalsand

**Solution.**

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

possible.

**Solution.** First, we simplify all square roots:

Second, we gather all terms :

**Exercise 4.10.** Rationalize the denominator.

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