Real Number System

Notes

Rational and Irrational Number

The union of the set of rational numbers and the set of irrational numbers is called the real numbers.The Number in the form \(\frac{p}{q}\), where p and q are integers and q≠0 are called rational numbers.Numbers which can be expressed in decimal form are expressible neither in terminating nor in repeating decimals, are known as irrational numbers.

Scientific Notation

Scientific notation is, essentially, a method for writing really big or really small numbers. It is called scientific notation because these huge numbers are often found in scientific work. For example, you might have the number 6000000000000. That’s really big, right? Unfortunately, it isn’t easy to tell exactly how big at first glance with all those zeroes stuck on the end. Instead, the number could be written as 6 * 1000000000000. Then you can change it.

Significant Figures

The significant figures of a number are digits that carry meaning contributing to its measurement resolution.

Surds

Surds are numbers left in 'square root form' (or 'cube root form' etc). They are therefore irrational numbers. The reason we leave them as surds is because in a decimal form they would go on forever and so this is a very clumsy way of writing them.

The Real Number System

A real number is a value that represents a quantity along a continuous line and defines the real number system geometrically. The real number include all the rational numbers, such as the integer -5, and the fraction 4/3 and all the irrational numbers.The union of the set of rational numbers and the set of irrational numbers is called the set of real numbers.Thus, the collection of all points on the number line can be thought of as the system of real numbers.