Starter Round to 1 decimal place This is the degree of accuracy (how accurate an answer is) Starter Round to 1 decimal place 5.18 15.09 187.55 90.05 8.97 6.49 Extension: Round to 1 significant figure. 5.2 15.1 187.6 90.1 9.0 6.5 5 20 200 90 9 6 This is also a degree of accuracy

To realise that answers in Mathematics are often not exact Exactly how accurate? Lesson Objective To realise that answers in Mathematics are often not exact

Key Words Upper Bound Lower Bound Rounding Error (Degree of) Accuracy The value at which something would be rounded up Upper Bound Lower Bound Rounding Error (Degree of) Accuracy Significant figure Decimal Place The lowest value something is before rounding The difference from the exact answer caused by rounding What something is rounded to

Answer these questions How old are you? What time is it? What’s the span of your hand? What is the value of π? How many students in this class? How many students in the whole school? How accurate are your answers?

The time is shown to 2 decimal places Degrees of Accuracy Quite often, we see numbers that aren’t exact. What is the degree of accuracy here? The time is shown to 2 decimal places

Bounds What is the lowest, and highest, values that this number could be if it is rounded to the nearest ten already? 65 Highest possible value (UPPER BOUND) 60 55 Lowest possible value (LOWER BOUND) 50 60 70

Bounds What is the lowest, and highest, values that this number could be if it is actually rounded to the nearest whole number already? 60.5 Highest possible value (UPPER BOUND) 60 59.5 Lowest possible value (LOWER BOUND) 59 60 61

What is the fastest possible time Usain Bolt completed the 100m in? What is the slowest? Extension: What would his fastest/slowest speed be? (assume the 100m track is exactly 100m – what would be the effect if it was measured to the nearest meter??) 9.575 seconds 9.585 seconds

Rounding Error So, the exact value of our number could be anything between 59.5 – 60.5 What effect could this have when we come to do some calculations?

Effect on calculations The dimensions are measured to the nearest cm 94.5cm 95.5cm Work out the upper and lower bounds for each dimension 95cm 70cm 69.5cm 70.5cm

Work out the upper and lower bounds for the perimeter 94.5cm 95.5cm Work out the upper and lower bounds for the perimeter Extension – Work out the upper and lower bounds for the area of the screen 95cm 70cm 69.5cm 70.5cm Perimeter Upper Bound – 332cm Lower Bound – 328cm Area UB – 6732.75cm² LB – 6567.75cm²

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