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Have you heard about calculus? It is yet another extension of math. Depending upon your field of interest in high-school, and later college, some of you will never get into full calculus but whether you decide on a career that will require it or not, it’s important to know some of the very simple basics of calculus. And the very basic is that of **rational numbers**.

Okay, so then what exactly are rational numbers? **Rational numbers are any number that can be written into a simple fraction.** For example, the number 1.5 can be written as ^{3}⁄_{2}. The fraction is a simple fraction making the number 1.5 a rational number. **NOTE:** The denominator cannot be “0”.

Let’s look at a few more examples. Let’s take the numbers 5, .001 and √2 to see if these numbers are rational numbers.

** Example 1:** 5 can be written as 5/1. It is a simple fraction so since it can be written into a simple fraction, it is a rational number.

** Example 2:** .001 can be written as 1/1000 so it too is a simple fraction making .001 a rational number.

** Example 3:** √2 ... Ah now, there is no simple fraction that would be the same as √2. Because of this √2 is NOT a rational number.

1.

Which of the following numbers is NOT a rational number?

14

1/4

40

√5

Answers (a) and (b) can be put into simple fractions and answer (b) is a simple fraction so they are all rational numbers. However, Answer (d) cannot be put into a simple fraction so it is not a rational number. Answer (d) is the correct answer

2.

Which of the following numbers is a rational number?

√11

1.333

√23

π

Answers (a) and (c) are square roots and they cannot be written as simple fractions. Because of this, they are NOT rational numbers. Answer (d) shows the symbol of pi (π). π = 3.14159... and it cannot be written into a simple fraction so it is not the correct answer either. However, Answer (b) can also be written as 1^{333}⁄_{1000}. As this includes a simple fraction, it is a rational number. Answer (b) is the correct answer

3.

Which of the following numbers is a rational number?

π

√17

-85

√37

Answer (a) shows the symbol of pi (π) which cannot be written into a simple fraction. Because of this, it is not correct. Answers (b) and (d) are square roots and they, too, cannot be written as simple fractions. Answer (c), however, can be written as -^{85}⁄_{1}. As this includes a simple fraction, it is a rational number. Answer (c) is the correct answer

4.

Which of the following numbers is a rational number?

√29

√2

√69

.432

Answers (a), (b) and (c) are all square root numbers and cannot, therefore, be written into a simple fraction. Answer (d) can be written as ^{432}⁄_{1000} which is a simple fraction. Answer (d) is the correct answer

5.

Which of the following numbers is NOT a rational number?

√41

.222

-16

3/4

Answers (b) and (c) can be put into simple fractions and answer (d) already is a simple fraction so these numbers are all rational numbers. However, Answer (a) cannot be put into a simple fraction as it is a square root. This means it is NOT a rational number. Answer (a) is the correct answer

6.

Which of the following numbers is NOT a rational number?

24

195

√73

.10

Answers (a), (b) and (d) can each be put into simple fractions making them all rational numbers. However, Answer (c) cannot be put into a simple fraction as it is a square root. This means it is NOT a rational number. Answer (c) is the correct answer

7.

Which of the following numbers is a rational number?

.543987543...

63

√19

.8954398658...

Answers (a) and (d) fall into the same category as does pi (π). They cannot be converted into simple fractions so they are not rational numbers. Answer (c) is a square root and it, too, cannot be written as a simple fraction. Answer (b) can be written into a simple fraction such as ^{63}⁄_{1} so it is a rational number. Answer (b) is the correct answer

8.

Which of the following numbers is NOT a rational number?

100

π

56

78

Answers (a), (c) and (d) can each be put into simple fractions making them all rational numbers. However, Answer (b) is pi which equals 3.14159... and it cannot be put into a simple fraction. Therefore, Answer (b) is the correct answer

9.

Which of the following numbers is a rational number?

1

3.14159...

√71

√53

Answer (b) is the number for pi (π) and pi (π) is NOT a rational number. Answers (c) and (d) are both square root numbers and cannot, therefore, be written into a simple fraction. Answer (a) can be written as ^{1}⁄_{1} which is a simple fraction. Answer (a) is the correct answer

10.

Which of the following numbers is a rational number?

.7906874197...

.348790...

.25

.165972...

Answers (a), (b) and (d) are all similar to pi (π). They cannot be turned into simple fractions. However, Answer (c) can be rewritten as ^{25}⁄_{100} or ^{1}⁄_{4} which is a simple fraction. Answer (c) is the correct answer