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

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

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 Round to the nearest

Section E – Rounding Numbers Round to the nearest Tenth Round to the nearest Hundredth

Calculate to 2 decimal places: ( )(0.82 – 0.57) 18.6 – (12.2 – 4.3) 5.2

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.

ExampleNo. of Sig Figs x 10 5

Write correct to 3 significant figures. Write correct to 3 significant figures.

Round to 2 significant figures. Round to 1 significant figures. 423 to 1 significant figures to 3 significant figures.

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

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

A crowd size is estimated at but was actually 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.