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8 Types of Number Expressing Numbers Numbers can be expressed in different ways. They can be represented numerically, e.g. 600, or in word form, e.g. six hundred. To convert from numerical form to word form, the non-zero digits of the places must be noted down and converted to their respective places’ word form. For example, 61,520 can be written as sixty-one thousand, five hundred and twenty. The six is in the ten-thousands’ place, the one is in the thousands’ place, the five is in the hundreds’ place, and the two is in the tens’ place. Since zero is in the units’ place, it is ignored. Similarly, 509,007 can be written as five hundred and nine thousand, and seven. Note that each three digits starting from the right are collected into units, tens and hundreds. The first three digits are written as they are, the next three digits are followed by the word ‘thousand’, the next three are followed by the word ‘million’, then ‘billion’, ‘trillion’, and so on. This method can also be used to convert words into numerical form. For example, “six hundred-billion” means that there are 3 + 3 + 3 + 3 = 12 digits in that number. So it can be written down as 600,000,000,000, or 6 followed by eleven 0s. Broad Sets of Numbers Real Numbers: These are the set of all numbers that are dealt with at IGCSE Level. This excludes imaginary numbers. The symbol ℝ may be used to represent this set. Integers: These are whole numbers, i.e. numbers without any fraction/decimal. They can be positive, negative, or zero. The symbol ℤ may be used to represent integers. Natural Numbers: These are the set of all positive integers, e.g. 1, 2, 3, … The symbol ℕ may be used to denote natural numbers. Rational and Irrational Numbers: Rational numbers include any real numbers that can be expressed as a fraction in the form of a/b, where a and b are whole numbers. Irrational numbers cannot be expressed in this way. All terminating and recurring decimals are rational. π is irrational; this is a constant that will be used in future chapters.