1. Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, 2004

2. Topic 1 – Number and Algebra 1.2 – Approximation, Significant Figures and Error

3. Section E – Rounding Numbers If the digit after the one being rounded off is less than 5 we round down. If the digit after the one being rounded off is 5 or more we round up. Round to the nearest 10 48 583 6746 Round to the nearest 100 452 37239 104792

4. Section E – Rounding Numbers Round to the nearest Tenth 3.01 4.153 7.2438 Round to the nearest Hundredth 6.238 4.0156 8.22446

5. Calculate to 2 decimal places: (2.8 + 3.7)(0.82 – 0.57) 18.6 – (12.2 – 4.3) 5.2

6. Significant Figures The numbers 1-9 are always significant. Zeros in the front are never significant. Zeros in the middle are always significant. Zeros in the back are only significant if they follow the decimal point and another significant figure.

7. ExampleNo. of Sig Figs 453 5057 5.00 0.007 20400 0.090 5.1 x 10 5

8. Write 278463 correct to 3 significant figures. Write 0.0076584 correct to 3 significant figures.

9. Round 5.371 to 2 significant figures. Round 0.0086 to 1 significant figures. 423 to 1 significant figures. 4.053 to 3 significant figures.

10. Use your calculator: Simplify to 3 significant figures (3.2 × 10 4 ) × (8.6 × 10 -16 )

11. Section I – Error and Percentage Error Error occurs due to rounding or approximations. Error = (approximate value – exact value) Percentage Error

12. A crowd size is estimated at 15000 but was actually 14869. Find the error & percentage error. You estimate a fence’s length to be 70 m and when you measure it, its true length is 78.3 m. Find the error and percentage error correct to one decimal place.