Types of number (integers, decimals, fractions, percentages, and surds)

Integers: Whole numbers that can be positive, negative or zero. Range from negative infinity to positive infinity.
Decimals: Numbers expressed in base 10, have an integer part and a fraction part separated by a decimal point. Example 0.75, 12.5 are decimals.
Fractions: Express part of a whole or a ratio of two numbers. They contain a numerator (above the line) and a denominator (below the line). Example 1/2, 5/7 are fractions.
Percentages: Represent proportions as parts out of 100, denoted by the symbol ‘%’. Example 25%, 100% are percentages.
Surds: Represent roots that cannot be expressed as an exact fractional power. Example, √2, √3 are surds, but √4 is not a surd as it simplifies to an exact integer of 2.

Understand how to convert between different types of numbers. For instance, moving from a fraction to a percentage, or from a decimal to a surd.
Conversion into decimal form is a common task: percentages, fractions, and square roots can all be expressed in this way.
Rounding numbers often comes into play, and can involve any type of number. Remember when to round up and when to round down.
Surds often cause difficulty as they are a less familiar number type. Remember their key features, such as having no exact fractional or decimal equivalent.

Be confident with the four operations (addition, subtraction, multiplication, division) for each of the number types: integers, decimal, fractions, percentages, and surds.
Ordering and comparing different types of numbers is a key skill: consider converting all numbers to the same type (often decimals) to aid comprehension.
Be aware of common mistakes like assuming that a larger denominator makes a fraction larger - this is a false assumption.
Practise a wide range of questions involving different types of numbers. This will build familiarity and confidence - key for exam success.