Integers and Types of Numbers

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Pre-Algebra › Integers and Types of Numbers

Questions 1 - 10

Which is a square number?

Explanation

Square numbers have one factor. If that factor is multiplied by itself, then the number becomes a perfect square. The only number in the selection that meets this requirement is . We can multiply twice to get the perfect square .

Which of the following is an odd number?

II.

III.

IV.

II, III, V

I, III, IV

II, V

I, III, V

II, III, IV

Explanation

Odd numbers are integers that have a ones digit that ends in , , , , or . Choices II, III, V are odd numbers because they have a ones digit of , , and respectively.

Which of the following is an integer?

$\sqrt {25}$

$2\pi$

$\textup{No integers are given.}$

Explanation

The correct answer will yield a whole number as a simplified answer. Integers cannot contain decimals quantities.

The only answer that will yield a whole number term is $\sqrt {25}$ since simplifying this root will yield $\pm5$ .

The correct answer is: $\sqrt {25}$

What kind of number is $\sqrt{16}$ ?

I. rational

II. irrational

III. integer

IV. imaginary

V. composite

I, III, V

II, IV

II only

III and V only

I and III only

Explanation

Even though it's a radical, we can simplify $\sqrt{16}$ .

$\sqrt{16}=4$

Check the answer.

The answer is .

is an integer and a composite number with factors of . Furthermore, it can be expressed a rational number $(4=\frac{4}{1})$ .

Thus, the final answer is I, III, V.

What number is found in the set of whole numbers but not in the set of natural numbers?

$\pi$

$\frac{1}{2}$

Explanation

Whole numbers start from and include all positive integers. On the other hand, natural numbers are all positive integers that we can count starting from . The only difference is that is found in whole numbers but not in the natural numbers series. Thus, is the correct answer.

Which is a prime number?

Explanation

A prime number is a number that havs factors of one and itself. Let's eliminate some choices.

A number divisible by will have a ones digit of or . So we eliminate .

Even numbers are having ones digit end in . So we eliminate

For the remaining , let's try the divisibility rule of . The sum of the digits add up to a multiply of is diisible by .

$21\rightarrow2+1=3$ This is good.

$39\rightarrow3+9=12$ This is divisible by .

$23\rightarrow2+3=5$ This fails as this is our answer.

What is a rational number?

Two integers that can be expressed in a fraction as long as the denominator is not zero.

Any kind of fraction

All real numbers

Only positive and negative integers.

Imaginary numbers

Explanation

For a number to be rational, the numerator and denominator have to be integers. The exception is the denominator must not equal zero. It can be negative, positive, or zero.

Which of these numbers is not a rational number?

$\pi$

$\frac{2}{3}$

$0.\overline{12121212}$

Explanation

A number is rational if it is possible to express it as a fraction with integers as the numerator and denominator. 25 and -1 are integers, and could be written as fractions: $\frac{25}{1}, \frac{-1}{1}$ . $\frac{2}{3}$ is already expressed as a fraction. At first glance,

$0.\overline{12121212}$ looks like an irrational number becasue it repeats forever. This is different from an irrational number because an irrational number will go on forever but without a repeating pattern. $0.\overline{12121212}$ could actually be expressed as the fraction $\frac{12}{99}$ . This leaves us with the correct answer of $\pi \approx 3.14159...$ which goes on forever \[is non-terminating\] but without any clear pattern or repeating part.

Which of the following is NOT an integer?

$\sqrt{3}$

Explanation

An integer is a number that has no decimals or fractions. They must be whole numbers whether positive, negative or zero. $\sqrt{3}$ is an irrational number which means it doesn't have a definite value. All the other choices have definite value.