Question

1. Which of the following is an irrational number? How do you know? Use key words and definitions to explain your answer choice.
a. 1632
b. 0.25
c. 0.0300300030000…
d. 0






2. Is the following example true or false? If false, give a counterexample. “The sum of two rational numbers is always rational. The sum of two irrational numbers is always irrational.”







3. Which of the following expressions is equivalent to 6(94)+7+(3+2)
a. 2+(3+7)+4(69)
b. 9(64)+2+(73)
c. (6+7)(94)+3+2
What properties of real numbers does this example show

Answer 1

Answer:

#1

Rational numbers can be shown in the form of p/q.

• a. 1632 - positive integer = rational
• b. 0.25 - terminating decimal = rational
• c. 0.0300300030000... - non-terminating decimal = irrational
• d. 0 - zero is rational

#2

The sum of two rational numbers is always rational.

• TRUE as it still can be shown as p/q.

The sum of two irrational numbers is always irrational.

• FALSE as in specific cases, when you sum the opposites of irrational numbers you get zero which is rational

#3

This question is incomplete or incorrect.

None of the choices is equivalent.

Answer 2

Answer:

1.

1632 can be written as 1632/1. Rational

0.25 can be written as 25/100. Rational

0.0300300030... cannot be written as fraction. Irrational

0 is also irrational

2. Sum of two rational number = rational number

Sum of two irrational number = Rational or irrational number

3. Incomplete