# Estimations and Limits of Accuracy

Students learn how to round a number to a significant figure.  They use this knowledge to estimate solutions by rounding and finding the limits of accuracy of rounded numbers.  As learning progresses they are challenged to calculate the upper and lower bounds in calculations.  This topic takes place in  Year 10 Term 2 and follows fractions and decimals.

##### Revision Lessons

Prerequisite Knowledge

• Recognise the value of a digit using the place value table.
• Round numbers to the nearest integer or given degree of accuracy not including decimal place or significant figure
• Calculate square numbers up to 12 x 12.

Success Criteria

• Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate
• Round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures
• Estimate answers; check calculations using approximation and estimation, including answers obtained using technology
• Use inequality notation to specify simple error intervals due to truncation or rounding
• Apply and interpret limits of accuracy, including upper and lower bounds

Key Concepts

• When rounding to the nearest ten, decimal place or significant figure students need to visualise the value at a position along the number line. For instance, 37 to the nearest 10 rounds to 40 and 5.62 to 1 decimal place rounds to 5.6.
• When a value is exactly halfway, for instance 15 to the nearest 10, by definition it is rounded up to 20.
• To estimate a solution it is necessary to round values to 1 significant figure in the first instance. However, students need to apply their knowledge of square numbers when estimating roots.

Common Misconceptions

• When rounding to a significant figure the values that are less significant become zero rather than being omitted. For instance, 435 to 1 s.f. becomes 400 rather than 4.
• Students often have difficulty calculating the upper bound of a rounded value. For instance the upper bound for a number rounded to the nearest 10 as 20 is 25 not 24.999.
• When using inequality notation to describe the limits of accuracy there can be confusion with the direction of the symbols.
• Students often have difficulty knowing which bound to use when calculating the limits of accuracy for division and subtraction problems.

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