To change a number into another number that is approximately the same value but is easier to work with. E.g. round 561 to the nearest 10 is 560.

Checking understanding of rounding

Maths

In this unit, pupils have learnt how to round to a given number of decimal places or significant figures and explored the effect of using rounded numbers for calculations. In the future unit, pupils will investigate the bounds and perform calculations to determine a best/worst case scenario.

The prior unit on place value allowed pupils to develop the skills needed to estimate and round values. By understanding the value of each digit, pupils can determine what other values are close to the original value. This unit continues the exploration of the infinite nature of sets of numbers.

This unit helps pupils understand rounding to different decimal places, and significant figures. Pupils will also learn how to truncate numbers and understand the contexts in which these skills are useful. The unit ends will an exploration of rounding and inequality errors.

Estimation and rounding

A (mathematical) statement that is thought to be true but has not been proved yet.

A degree of accuracy shows how precise a number or measurement is.  E.g. to the nearest cm, nearest 10, 1 d.p., etc.

Securing understanding of rounding

Rounding to three decimal places

Rounding to any number of decimal places

Significant figures are the digits in a number that contribute to the accuracy of the number. The first significant figure is the first non-zero digit.

Rounding integers to one significant figure

Rounding integers to significant figures

Rounding decimals to significant figures

A degree of accuracy shows how precise a number or measurement is.  E.g. to the nearest cm, nearest 10, 1 s.f., etc

Degrees of accuracy

A quick estimate for a calculation is obtained from using approximate values, often rounded to 1 significant figure.

Significant figures are the digits in a number that contribute to the accuracy of the number.

Estimating numerical calculations

Checking by estimating

Truncation is the simplifying a number by 'cutting off' one or more of the digits and replacing them with zeros if necessary to preserve place value.

A degree of accuracy shows how precise a number or measurement is.

Truncating

An overestimate is an estimate for a calculation which is greater than the exact answer.

An underestimate is an estimate for a calculation which is less than the exact answer.

Overestimating vs underestimating

Significant figures are the digits in a number that contribute to the accuracy of the number

Rounding errors

A range of values where every value in the range estimates to the given value.

An error interval for a number $$x$$ shows the range of possible values of $$x$$.  It is written as an inequality $$a ≤ x < b$$

Inequality notation to express error

An error interval for a number $$x$$ shows the range of possible values of $$x$$. It is written as an inequality $$a ≤ x < b$$

Estimation and rounding

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These lessons will be removed by end of Summer Term 2025.