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

Rounding errors

Maths

Checking understanding of rounding

Securing understanding of rounding

Rounding to three decimal places

Rounding to any number of decimal places

Rounding integers to one significant figure

Rounding integers to significant figures

Rounding decimals to significant figures

Degrees of accuracy

Estimating numerical calculations

Checking by estimating

Truncating

Overestimating vs underestimating

Inequality notation to express error

Using inequality notation for errors in calculations

Problem solving with estimation and rounding

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

Smallest integer = 674, largest integer = 684

Smallest integer = 670, largest integer = 680

Smallest integer = 670, largest integer = 690

Smallest integer = 675, largest integer = 684

State the smallest and largest integers that round to 680 when rounded to the nearest 10.

Smallest integer = 480, largest integer = 514

Smallest integer = 490, largest integer = 509

Smallest integer = 500, largest integer = 510

Smallest integer = 485, largest integer = 514

Smallest integer = 490, largest integer = 514

State the smallest and largest integers that round to 500 when rounded to the nearest 20.

Smallest integer = 675, largest integer = 725

Smallest integer = 674 largest integer = 724

Smallest integer = 725, largest integer = 734

Smallest integer = 675, largest integer = 724

Smallest integer = 674, largest integer = 725

State the smallest and largest integers that round to 700 when rounded to the nearest 50.

An advert for a magazine says 37 000 people buy the magazine rounded to the nearest 1000. The fewest people who buy the magazine is {{ }} people.

Andeep: $$2.39\times5.78=2.4\times5.8=13.9$$ km$$^2$$ 

Laura: $$2.39\times5.78= 13.814... = 13.8$$ km$$^2$$ 

Jun: $$2.39\times5.78= 13.8142 = 13.9$$ km$$^2$$ 

Lucas: $$2.39\times5.78= 13.8142 = 13.8$$ km$$^2$$ 

A plot of rectangular land measure 2.39 km (1 d.p.) by 5.78 km (1 d.p.). Five pupils work out the area of the plot of land. Whose working out and answer shows the most accurate answer to 1 d.p?

A large plot of land has an area of 20 km². A small, rectangular lake with lengths 3.254 km by 4.814 km is planned, leaving the rest of the land as grass. Work out the area of grass to 1 d.p.

An __________ is any positive or negative whole number and zero.

When a number is rounded to the nearest integer it is 4. Select the possible unrounded numbers. 

Round each number in the calculation to 1 significant figure and calculate the answer. $$\frac{89.7+9.58}{5.34+4.58}$$. Give your answer as an integer.

Rounding errors

Lesson outcome