Real Numbers

Mathematics originated from the process of expressing what through symbols as numbers?

According to the Greek philosopher Aristotle, the formal beginning of mathematics started with practice among which community?

Number-based mathematics was created approximately how many years before the birth of Jesus Christ?

Who first introduced the concept of $0$ and the decimal number system?

Who expanded the concepts of zero, negative, real, integer and fractional numbers that the Arabian mathematicians later took on?

Expressing numbers by decimal fractions is credited to—

In which century did Muslim mathematicians first introduce irrational numbers in the form of square roots for solving quadratic equations?

Around $500$ A.D., which group felt the necessity of irrational numbers (especially $\sqrt{2}$) for geometrical drawing?

In which century did European mathematicians give real numbers complete shape by systematization?

Which group of mathematicians expanded the concept that Arabian mathematicians later took on during the Medieval Age?

Which of the following is the set of natural numbers?

Which of the following is a prime number?

Which of the following is a composite number?

How many prime numbers are there from $1$ to $10$?

Which list contains only prime numbers?

Which list contains only composite numbers?

Two integers are said to be mutually prime if their GCD is—

Which pair is mutually prime?

Which description best fits integers?

Which of the following is NOT an integer?

Which number is an integer but not a natural number?

A fraction $\frac{p}{q}$ is called proper when—

Which of the following is an improper fraction?

For a fraction $\frac{p}{q}$, which condition must hold?

Which of the following is a proper fraction?

A rational number has the form $\frac{p}{q}$ where—

Which of the following is a rational number?

All integers are—

Which of the following is NOT a rational number?

Any rational number can be expressed as the ratio of two—

An irrational number CANNOT be expressed as—

Square root of which number is irrational?

Which of the following is irrational?

$\sqrt{2}$ is approximately—

$\sqrt{3}$ is approximately—

$\sqrt{5}$ is approximately—

In the proof that $\sqrt{2}$ is irrational, $\sqrt{2}$ is initially assumed as—

Which of the following is NOT an irrational number?

Decimal fractions are classified into how many types?

Which of the following is a finite decimal fraction?

$0.333\dots$ is a—

Which of the following is an infinite non-repeating decimal?

Finite and repeating decimal fractions are—

Infinite non-repeating decimal numbers are—

$1.\overline{23}$ means—

In a repeating decimal fraction, when a single digit repeats, the dot is placed—

When more than one digit repeats, the dot is placed—

A repeated decimal fraction where every digit after the decimal point repeats is called—

$4.235\overline{112}$ is classified as—

The number of digits in the repeating part of a repeating decimal is always—

Real numbers include—

Which of the following is NOT a real number?

Which of the following is a positive number?

Which of the following is a negative number?

Non-negative numbers include—

Which of the following is NOT a non-negative number?

If $a, b$ are real, then $a + b$ is—

For real numbers $a, b$, $a + b$ equals—

The associative property of addition states—

The distributive property states—

The additive identity in real numbers is—

The multiplicative identity in real numbers is—

For any real $a$, $a + (-a)$ equals—

For any nonzero real $a$, $a \cdot \frac{1}{a}$ equals—

If $a, b$ are real, which of the following is always true?

If $a, b, c$ are real and $a < b$, then $a + c$ compared with $b + c$ is—

If $a < b$ and $c > 0$, then $ac$ compared with $bc$ is—

If $a < b$ and $c < 0$, then $ac$ compared with $bc$ is—

When $1$ is added to the product of four consecutive natural numbers, the result is—

$x(x+1)(x+2)(x+3) + 1$ equals—

$1 \cdot 2 \cdot 3 \cdot 4 + 1$ equals—

If $a, b, c, d$ are four consecutive natural numbers, which of the following is a perfect square?

Product of any two consecutive even integers is divisible by—

Product of three consecutive natural numbers is always divisible by—

If $a, b$ are integers, what should be added to $a^2 + b^2$ to obtain a perfect square?

If $a, b$ are two consecutive even numbers, which of the following is odd?

The square root of a natural number that is NOT a perfect square is always—

$\frac{1}{3}$ equals—

$\frac{3}{11}$ equals—

$\frac{95}{37}$ equals—

$\frac{5}{3}$ as a decimal is—

$0.\overline{3}$ as a simple fraction equals—

$0.\overline{24}$ as a simple fraction equals—

$0.\overline{2}$ as a fraction equals—

$0.1\overline{3}$ as a fraction equals—

$0.\overline{35}$ in simplest form equals—

When converting $0.\overline{ab}$ (both digits repeating) to a fraction, the denominator is—

For a decimal of the form $0.p_1 p_2 \overline{q_1 q_2}$ (2 non-repeating, 2 repeating digits), the denominator is—

In converting $42.34\overline{78}$ to a common fraction, the raw denominator (before simplification) is—

$0.\overline{6}$ as a fraction equals—

Two repeating decimals are called "similar" when—

$12.\overline{45}$ and $6.\overline{32}$ are—

$0.\overline{3456}$ and $7.4\overline{5789}$ are—

In Example 8 of the chapter, $5.\overline{6}$ is converted into its similar form as—

When creating similar repeating decimals, the number of digits in the repeating part of each must be equal to—

The number of digits in the non-repeating part of each similar form equals—

In the addition of similar repeating decimals, any carry produced at the leftmost digit of the repeating part is—

In the subtraction of repeating decimals, any borrow at the leftmost repeating digit is—

The sum or difference of repeating decimals is—

Example 10 of the book gives $3.\overline{89} + 2.1\overline{78} + 5.89\overline{798}$ as—

Subtracting $5.2\overline{4673}$ from $8.2\overline{43}$ gives—

Subtracting $16.4\overline{37}$ from $24.45\overline{645}$ gives—

$4.\overline{3}$ as a fraction equals—

$5.\overline{7}$ as a fraction equals—

$4.\overline{3} \times 5.\overline{7}$ equals—

$0.\overline{28} \times 42.\overline{18}$ equals—

To multiply or divide repeating decimals, it is easier to first convert them into—

From Example 19 of the chapter, $9.4\overline{5} \div 2.\overline{863}$ equals—

Value of $\sqrt{2}$ up to three decimal places is—

Approximate value of $\sqrt{13}$ up to three decimal places is—

$\sqrt{2}$ is classified as—

For $4.4623845\dots$, the value up to $3$ decimal places is—

For $4.4623845\dots$, the approximate value up to $4$ decimal places is—

When approximating to a given decimal place, if the next digit is $5$ or more, then—

Value of $4.4623845\dots$ up to $1$ decimal place is—

Approximate value of $4.4623845\dots$ up to $1$ decimal place is—

Between any two different real numbers, how many rational numbers exist?

How many real numbers lie between $0$ and $1$?

The sum of two rational numbers is always—

The sum of a rational and an irrational number is—

$\sqrt{2} + (-\sqrt{2})$ equals—

$\sqrt{2} + \sqrt{3}$ is—

$\frac{22}{7}$ is used for $\pi$ as—

$\pi = 3.14159\dots$ approximated to two decimal places is—

An irrational number between $\sqrt{3}$ and $4$ can be—

Between $0.12$ and $0.31$, which of the following is irrational?

Which of the following is a non-terminating, non-repeating decimal?

If $a = \sqrt{3}$ and $b = \sqrt{12}$, then $ab$ equals—

If $a = \sqrt{3}$ and $b = \sqrt{12}$, then $\frac{a}{b}$ equals—

If $a = \sqrt{3}$ and $b = \sqrt{12}$, then $a + b$ is—

An irrational number between $\sqrt{3}$ and $\sqrt{12}$ is—