Understanding numbers and the number system
Understanding Numbers and the Number System
Basics of Numeracy
- Place value is the value of each digit in a number based on its position. For example, in the number 231, the 2 is in the hundreds position.
- Positive numbers are greater than zero, while negative numbers are less than zero. Zero is neither positive nor negative.
- Fractions represent parts of a whole. They are made of a numerator (top) and a denominator (bottom). Simplify fractions where possible.
- Decimals are another way to represent fractions and percentages. Understand how to convert between fractions, decimals and percentages.
- Percentages are fractions out of 100. They are often used to represent proportions and comparisons.
Operations
- Addition is the process of combining numbers. The result is called the sum.
- Subtraction is finding the difference between two numbers. The result is known as the difference.
- Multiplication is the process of repeated addition. The result is called the product.
- Division is the process of distributing a set of numbers equally. The answer is known as the quotient.
Complexity of Numbers
- Square numbers result from multiplying a number by itself.
- Square roots are the inverse operation of squaring a number.
- Cubed numbers are figures that arise from multiplying a number by itself twice.
- The cube root is the reverse operation of cubing a number.
- Prime numbers are numbers that have only two distinct positive divisors: 1 and itself. The first few prime numbers are: 2, 3, 5, 7, 11, and 13.
- Composite numbers are numbers that have more than two distinct positive divisors.
Number Types
- Integers are whole numbers, both positive and negative, including zero.
- Rational numbers are numbers that can be written as a ratio of two integers. All integers, fractions, and decimals (that aren't repeating or never-ending) are examples of rational numbers.
- Irrational numbers are numbers that cannot be expressed as a ratio of two integers. They are non-repeating, non-terminating decimals.
- Real numbers comprise all rational and irrational numbers. In essence, real numbers include every number that exists on the number line.
Number Sequences
- Identify arithmetic sequences, which have a constant difference between numbers.
- Identify geometric sequences, where each term after the first is found by multiplying the previous term by a fixed, non-zero number.
- Recognise Fibonacci sequences, where each number is the sum of the two preceding ones.
- Calculate the nth term of an arithmetic sequence.