Grade A Upper and Lower Bounds Calculate upper

Grade A Upper and Lower Bounds Calculate upper and lower bounds. If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Key Vocabulary Error Interval 1 Significant Figure Limits of Accuracy Upper Bound Lower Bound

Limits of Accuracy Nothing that is measured can be 100% accurate. Whether you are using a ruler, a protractor, a thermometer or a set of kitchen scales, there will always be an error of ± half the unit of accuracy used. Quantity given to the nearest. . . Minimum value Maximum Value 0. 1 (to 1 decimal place) Given value – 0. 05 Given value + 0. 05 Whole Number Given value – 0. 5 Given value + 0. 5 Ten Given value – 5 Given value + 5 Hundred Given value – 50 Given value + 50 Thousand Given value – 500 Given value + 500

Upper & Lower Bounds The following numbers have been rounded to two significant figures. Find the upper and lower bounds for each value. (a) 23 Upper Bound = 23. 5 Lower Bound = 22. 5 (b) 0. 56 Upper Bound =0. 565 Lower Bound = 0. 555 Upper Bound = 835 Lower Bound = 825 (c) 830 Upper Bound = 205 Lower Bound = 195 (d) 200

Upper & Lower Bounds The following numbers have been rounded to two decimal places. Find the upper and lower bounds for each value. (a) 6. 17 Upper Bound = 6. 175 Lower Bound = 6. 165 (b) 0. 40 Upper Bound =0. 405 Lower Bound = 0. 395

Now you try: The following numbers have been rounded to two significant figures. Find the upper and lower bounds for each value. (a) 78 (b) 0. 91 (c) 0. 011 (d) 6000 The following numbers have been rounded to two decimal places. Find the upper and lower bounds for each value. (e) 23. 55 (f) 0. 82

Now you try: The following numbers have been rounded to two significant figures. Find the upper and lower bounds for each value. (a) 78 Upper Bound = 78. 5 Lower Bound = 77. 5 (b) 0. 91 Upper Bound =0. 915 Lower Bound = 0. 905 (c) 0. 011 Upper Bound = 0. 0115 Lower Bound = 0. 0105 (d) 6000 Upper Bound = 6050 Lower Bound = 5950 The following numbers have been rounded to two decimal places. Find the upper and lower bounds for each value. (e) 23. 55 Upper Bound = 23. 555 Lower Bound = 23. 545 (f) 0. 82 Upper Bound = 0. 825 Lower Bound = 0. 815

Reason and Explain The radius of a circle is 6. 5 cm to one decimal place. (a) Calculate the minimum perimeter of the circle. (b) Calculate the maximum area of the circle.

Reason and Explain The radius of a circle is 6. 5 cm to one decimal place. (a) Calculate the minimum perimeter of the circle. (b) Calculate the maximum area of the circle. Upper Bound 6. 55 cm Lower Bound 6. 45 cm (a) Minimum diameter = 2 x 6. 45 cm = 12. 9 cm Circumference = π x 12. 9 = 40. 53 cm Minimum perimeter = 40. 53 cm (b) Maximum radius = 6. 55 cm Maximum Area = π x 6. 55² = 134. 78 cm²

Reason and Explain A car is driving a distance of 160 miles correct to the nearest 10 miles. The car is travelling for 4 hours correct to the nearest hour. Calculate the maximum speed of the car.

Reason and Explain A car is driving a distance of 160 miles correct to the nearest 10 miles. The car is travelling for 4 hours correct to the nearest hour. Calculate the maximum speed of the car. Distance: Upper Bound = 165 miles Lower Bound = 155 miles Time: Upper Bound = 4. 5 hours Lower Bound = 3. 5 hours Speed = Distance ÷ Time With division, we get the largest answer when we divide the biggest number by the smallest number. Maximum speed = 165 ÷ 3. 5 = 47. 1 m. p. h