What's My Type? Trivia Quiz

Answer: Integer

Integers are also called whole numbers (their name coming from the Latin word for whole), and come in several subdivisions. The natural numbers, also called counting numbers, are positive numbers: 1, 2, 3, etc.; zero is also an integer, as are the additive inverses of the natural numbers. An additive inverse is a number you can add to any given number to get an answer of 0.

The example used, -3, is the additive inverse of 3.

Answer: Rational number

As their name suggests, rational numbers can be written as a ratio or quotient of two integers. They are also called fractions, but the mathematical concept is a bit more precise than the more general use of the term fraction. As well as being written in the familiar ratio form, they can be written as decimal numbers, showing their equivalent value in terms of the place values 0.1, 0.01, etc.

They can have their form changed by performing the indicated division - when you divide 3 by 4, your answer is 0.75, the decimal form of the fraction 3/4. (Decimals are often multiplied by 100 to give their value as a percentage - in this case, that would be 75%.) Any rational number can be written as a decimal that either terminates (you get an exact answer after some time) or repeats (the same number or group of numbers starts to appear cyclically).

The fraction one-third is 0.3333333, repeating forever; the fraction one-seventh is 0.142856142856, repeating forever.

Answer: Compound number

A compound number, sometimes also called a composite number or a mixed number, has both an integer part and a rational part. In this case, the integer is 2, the fraction 0.5 (or 1/2 - the compound number could also be shown as 2 1/2).

Answer: Prime number

A prime number is a positive integer larger than 1 which has no factors other than itself and 1. In other words, when you divide it by any number smaller than itself, your answer is a compound number, not an integer. The smallest prime number is 2, and it is also the only even prime number (since all other even numbers are divisible by 2). For technical reasons, the number 1 is not considered a prime number - that is why the definition includes the clause about primes being greater than 1.

Answer: Composite number

A composite number is a positive integer which has at least one factor (other than 1) which is smaller than itself. In this case, both 2 and 3 are factors of 6, since 6 divided by 2 is 3, and 6 divided by 3 is 2. They are called the prime factors of 6, because they are both prime numbers. Any composite number can be written as the product of prime numbers, although sometimes it takes a lot of them: 72, for example, is 2 x 2 x 2 x 3 x 3.

Answer: Square number

A square number is one which can be written as the product of two identical factors. In this case, 4 can be written as 2 x 2, so it is said to be the square of 2. The square of 3 is 9, the square of 4 is 16, and so on. If you take a number of dots equal to a square number, it is possible to arrange them into a square shape with the number of dots on each side being the number of which it is the square.

Interestingly, square numbers can also be created by adding up odd numbers sequentially: 1+3 = 4; 1+3+5 = 9; 1+3+5+7 = 16, and so on.

Answer: Irrational number

Unfortunately, the symbol used to show a square root cannot be replicated here - it looks like a tick whose top end is attached to a horizontal line that extends over the number in question. This symbol indicates that we are dealing with a number that can be multiplied by itself to get the number under the square root sign.

The square root of 4 is 2, since 4 is 2 squared (2x2 = 4). But if the number under the sign is not a perfect square, then it is impossible to show it exactly as a whole number or fraction. Approximations can be shown, but if you write the number down in decimal form, then you will find that the pattern of numbers never repeats. Since the number cannot be written as a ratio of integers, it is called irrational.

Answer: Transcendental number

A transcendental number is defined as one which is not algebraic - that is, there is no way to write a polynomial equation using rational coefficients which has the stated number as a solution. When you write them in decimal form, the decimal goes on forever without repeating the pattern of numbers.

This makes them sound like irrational numbers, and the real transcendental numbers are also irrational. Many irrational numbers, however, can be defined using an algebraic equation: x^2 = 2, for example, has the square root of 2 as a solution.

This is not the case for numbers like e and pi, which is probably the most familiar transcendental number, since it is used in calculations involving circles. Transcendental numbers are often identified using Greek letters, or by the name of the mathematician who first demonstrated its existence or explored its properties in depth.

The number e gets its symbol from the name of the great mathematician Leonhard Euler.

Answer: Imaginary number

Imaginary numbers (which are very important in electronics applications, as well as being of mathematical interest just for their intriguing behavior) are multiples of the number i, which represents the number which, when multiplied by itself, gives -1 as an answer. For all real numbers, when you multiply the number by itself you get a positive answer. Imaginary numbers are the solutions of equations such as x^2 = -4, the solutions of which are 2i and -2i.

Answer: Complex number

Complex numbers have a real part (in this case, 2) and an imaginary part (in this case, 5i). Sometimes it is useful to consider real numbers as composite numbers whose imaginary component is 0i (3 is 3+0i), and pure imaginary numbers as composite numbers whose real component is 0 (5i is 0+5i). Now, it's time to finish before we start considering what composite numbers look like with transcendental components!