Numerical Properties and Rounding

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infoWhy this? Prime factorisation, estimation, bounds, and error intervals deepen understanding of number structure and numerical uncertainty. They enable us to communicate the range of possible values behind rounded measurements and assess the reliability of calculations.

scheduleWhy now? Earlier work established prime factors, significant figures, rounding, and truncation. Year 9 brings these ideas together so that we can reason with bounds and accuracy in later measurement, algebraic, and compound-measure problems.

A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself.
Every integer greater than 1 can be expressed uniquely as a product of prime numbers, apart from the order of the factors.
Rounding a number to one significant figure means expressing it using only its most significant non-zero digit, adjusting the value according to standard rounding rules.
Estimating answers to calculations by rounding to one significant figure can give a quick approximation of the result.
The upper bound of a rounded number is the upper endpoint of the interval of values that could have produced the rounded number.
The lower bound of a rounded number is the lower endpoint of the interval of values that could have produced the rounded number.
Bounds are often used when a value is given to a certain degree of accuracy, such as the nearest integer, decimal place, or significant figure.
Error interval notation is a way of expressing all possible values a rounded number could represent, typically using inequalities.

rocket_launchYou must be able to

Express a composite number as a product of its prime factors, using index notation where appropriate.
Round numbers to one significant figure and use these rounded values to estimate the result of calculations, including addition, subtraction, multiplication, and division.
Determine the upper and lower bounds for a value rounded to a given degree of accuracy, such as the nearest integer, decimal place, or significant figure.
Write the error interval for a value rounded to one decimal place using correct inequality notation.

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