Numerical Properties and Rounding

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infoWhy this? Prime factorisation exposes the multiplicative structure of integers, while significant figures and truncation develop control over numerical accuracy. Together, these ideas strengthen estimation, simplification, and the clear communication of approximate values.

scheduleWhy now? Building on Year 7 factors, powers, roots, and decimal-place rounding, this unit introduces more general methods and notation. It prepares us for advanced index work, standard form, estimation, and bounds.

A square number is the product of an integer multiplied by itself. For example, 4 is a square number because `4 = 2^2 = 2 \times 2`.
A cube number is the product of an integer multiplied by itself twice. For example, 8 is a cube number because `8 = 2^3 = 2 \times 2 \times 2`.
A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself.
A multiple of a number is the product of that number and an integer.
A factor of a number is a whole number that divides exactly into that number with no remainder.
The lowest common multiple (LCM) of two or more numbers is the smallest positive integer that is a multiple of each given number.
The highest common factor (HCF) of two or more numbers is the largest number that divides exactly into each of them.
Rounding is the process of adjusting a number to a specified degree of accuracy, such as the nearest integer, 10, 100, 1000, decimal place, or significant figure.
Truncating a number means shortening it to a specified number of significant figures without rounding.
The first significant figure is the first non-zero digit, while zeros between significant digits or after a decimal point can also be significant.
Any whole number greater than 1 can be expressed as a product of its prime factors (prime factorisation).

rocket_launchYou must be able to

Round a number to any given number of significant figures.
Truncate a number to any given number of significant figures.
Express a number as a product of its prime factors, using index notation where appropriate.

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